Yukawa’s Prediction of the Meson
by
LAURIE
M. BROWN*
1. Introduction
In October 1934, at a meeting of the Osaka Branch of the PhysicoMathematical Society of Japan, Hideki Yukawa proposed a new
theory of nuclear forces involving the exchange between neutron and
proton of an electrically charged “heavy quantum”.l Yukawa’s theory
is known today as the meson theory of nuclear forces and his “heavy
quantum” is called the meson.2 The theory provided a fundamental
explanation for the charge-exchange nuclear force that Werner
Heisenberg had proposed in 1932 and had associated with the ex. ~ the same
change of an electron between a neutron and a p r ~ t o n In
paper Yukawa suggested an alternative form of Enrico Fermi’s betadecay theory and showed that the two forms were phenomenologically
equivalent in the treatment of nuclear beta decay, although Yukawa
used the meson as an intermediary in beta decay and clearly distinguished the “strong” nuclear binding force from the “weak” force
responsible for radioactive-beta d e ~ a y . ~ * ~
Yukawa’s meson thus played a dual role: it carried energy,
momentum, and electric charge between neutron and proton, producing a strong nuclear force, and it decayed weakly (i.e., with small
probability) into electron and antineutrino, or positron and neutrino,
providing a mechanism for nuclear beta decay. Yukawa showed that
mesons would never be emitted in ordinary nuclear transformations
(radioactive decays and low-energy nuclear reactions), but that they
could materialize in nuclear processes involving sufficient energy release, such as those occurring in the interactions of cosmic rays. Produced this way, the mesons would either be absorbed by matter, or
they would themselves decay by the beta-decay process.
* Department of Physics and Astronomy, Northwestern University, Evanston, Ill. 60201, USA.
The author is grateful for partial support of this work by a grant from the National Science
Foundation.
Cmrovrus 1981: vol. 2 5 : pp. 71-132
72
Laurie M . Brown
The meson theory, therefore, predicted the existence of a new type
of elementary particle with well-defined observable properties, a particle which could be produced in a free state only in a regime of much
higher energy than was available in the nuclear laboratory at that
time. Yukawa’s work thus went beyond the theory of nuclear forces
and directed attention toward the field of high energy, or elementary
particle, physics, which has ever since been on the leading edge of
fundamental physics.
In treating the emission of electron and neutrino, Yukawa followed
Fermi’s lead and used the method of “second quantization”,6 but his
first treatment of the strong nuclear binding force was built as an
analogy to the semi-classical electromagnetic theory. In this version of
meson theory, protons and neutrons interact by means of “classical”,
but charge-carrying, meson fields. The nuclear force arises from the
exchange of mesons between non-relativistic protons and neutrons in
the same manner as the electrostatic Coulomb force arises from the
exchange of light quanta between slowly moving charges. Soon, however, Yukawa and his collaborators formulated meson theory as a
completely quantized field theory,’ about the same time that others,
outside of Japan, took notice of Yukawa’s work.
The article in which Yukawa proposed the meson is remarkable for
its simplicity, effectiveness, and comprehensiveness, although it was
the first original published work of a young physicist educated entirely
in Japan, where up to that time little research-in modem physics had
been done. His was the most fundamental scientific work of modern
times to be accomplished by an Oriental. Yukawa’s Nobel Prize of
1949 was only the second awarded to an Asian scientist (after Raman,
of India) and the first to be awarded to a Japanese.
The theory, published in February of 1935, went unnoticed for
more than two years,*?’ until observational evidence for particles of
intermediate mass in the cosmic rays began to be compelling.1° In July
of 1937 Yukawa suggested that “at least a part of the penetrating
component” consisted of mesons.” After noting several properties of
the new particles that agreed with those predicted for the meson, he
concluded: “this suggestion will not be altogether meaningless as a
possible explanation for the hard component of the cosmic ray, since
there seems to be no alternative for the time being.”
The cosmic ray particles of intermediate mass that first excited
YukawasS Prediction of (he Meson
73
world-wide interest in the meson theory were not, in fact, the mesons
of Yukawa. They turned out to be charged particles of half-integral
spin and to interact only weakly with nucleons. Resembling heavy
electrons in most respects, these particles (positive and negative) are
now called muons. More than a decade was to elapse before the true
discovery of the meson and the identification of the muon as one of its
possible decay products; meanwhile, it was generally assumed that the
meson of Yukawa had been observed.’*
The misidentification of the muon as the meson responsible for both
nuclear forces and nuclear beta decay, as it was thought, greatly encouraged the development of meson theory.I3 Many variants of the
theory were proposed and investigated in the attempt to reconcile the
properties of the meson needed for nuclear forces with the observed
properties of the muon. In recalling this period, Oppenheimer was to
say, “All of this, of course, later turned out to be nonsense. No one
had ever predicted these cosmic-ray mesons. No one knew what they
were; no one understands their existence today; no one has a good
argument as to why they should exist, nor have the properties they
have”14 and Hans Bethe wrote in 1954 that “The history of the subject of mesons and nuclear forces is an example. . . of both the wisdom
and the folly of scientist^."^^ Although it may be true that the meson
theory of nuclear forces gave “no serious quantitative results for about
twenty years”,16 there is little doubt that it led to important progress
in the study of elementary #articles, the cosmic rays, the quantum field
theory, as well as providing at least a qualitative understanding of the
nuclear force. The remarks of Bethe and Oppenheimer reveal the
scientist’s impatience at the pace of discovery and its application, but
they lack historical insight.
Even for some time after the experimental discoveries of the neutron and the positron in 1932 the term elementary particle meant
something external and immutable - a primordial atom. During the
1920’s and early 1930’s every effort was made to construct theoretically all matter, including the nucleus, out of just two elements, the
electron and the proton, often referred to simply as negative and
positive electricity. However, when Heisenberg began to realize that
his “composite” neutron behaved very much like the “elementary”
proton, the groundwork was laid for a thorough revision of the concept elementary. Likewise, the ghostly hole in the “sea” of negative
74
Laurie M . Brown
energy electrons, Dirac’s positron, was found to be as substantial as its
sister electron. Yukawa’s heavy quantum was never a hole, but a
massive charged particle that could be created singly (like a photon);
its virtual creation and subsequent annihilation was the mechanism of
the nuclear force - a further significant modification of the traditional
particle conception.
The present article began its life as an analysis of the nuclear force
problem in the early 1930’s and of Yukawa’s theoretical proposal for
its solution. As I came to realize the scope of Yukawa’s originality and
was struck by the failure of his brilliant seniors and contemporaries in
the West to arrive at any comparable solution, I began to ask what
cultural determinants (whether social, psychological, philosophical, or
esthetic) might have played a role either in Yukawa’s achievement or
his counterparts’ lack of the same. This was unfamiliar ground to me,
as it would be for other natural scientists or some historians of science.
This cultural puzzle (how young Yukawa could find a solution that
evaded Bohr, Heisenberg, Pauli, Fermi - not to mention Bethe,
Peierls, et al.) suggested another. Why did these same physicists so
rapidly become true believers in the meson theory, following the discovery of the muon in 1937? And it was, after all, not even the right
particle.
My treatment alternates between the physics and the persons and
institutions that made it. Sections 2 and 3 are concerned with
Yukawa’s family, schooling, and early cultural influences, and with his
perception of the important problems of physics when he graduated
from Kyoto University in 1929 and began research. Sections 4 and 5
are, respectively, studies of Heisenberg’s papers on nuclear structure
and Fermi’s theory of B decay. Section 6 follows Yukawa to his position as Lecturer at the new Science Faculty of Osaka University, his
contact with nuclear experimentalists there, the beginning of elementary particle research in Japan, and the gradual emergence of the idea
of the meson theory of nuclear forces.
In Sections 7 and 8 I draw out the physical and mathematical content of Yukawa’s first meson article: the meson is an intermediary, or
virtual particle, in both strong and weak nuclear interactions; it is
predicted to be an observable radioactive constituent of the cosmic
rays. Section 9 considers “the meaning of the meson,” as an illustration of a new methodology in elementary particle physics; as a case
Yukawas’s Prediction of fke Meson
75
study about a “scientifically developing” country; as an example of
social and psychological inhibition or stimulation. The rapid acceptance of the meson theory after the cosmic ray discovery of the muon is
discussed briefly in Section 10. Appendix I lists some standard as well
as some unusual sources; Appendix I1 is an English translation of
Yukawa’s first publication, the introduction to his Japanese translation of Heisenberg’s papers on nuclear structure.
2. The traveler sets out
Hideki Yukawa was born in Tokyo on January 23, 1907. A year later
he moved with his family to Kyoto when his father, Takuji Ogawa, left
a staff position in Tokyo with the Bureau of Geological Survey to
become Professor of Geography at Kyoto University.*’ It was in this
ancient capital and center of Japanese culture, therefore, that Yukawa
grew up and received his schooling.
The autobiography of Yukawa’s early years, The Traveler, conveys
some of the flavor of his Kyoto childhood.l* The family was a large
one, as there were seven children (Hideki being the fifth), the parents,
and three grandparents living together. Hideki’s mother, Koyuki, ran
the household and spent nearly all of her time serving the family.
Yukawa remembers her as hard-working and enjoying few pleasures
aside from the joy she took‘in her children. His father, a busy professor, dressed formally and each day was brought to the University in a
jinrickshaw .
A strong tradition of learning on both sides of Yukawa’s family was
transmitted to Hideki and his brothers.19 Takuji Ogawa was the second son of a Confucian scholar, Nanmei Asai, who had taught in a
school for the sons of the samurai of TanabC-han ca feudal clan). After
the Meiji Restoration of 1868 and the formal abolition of the samurai
class, he opened his own private school in the country. Yukawa’s
maternal grandfather, Komakitsu Ogawa, had himself been a samurai
serving at the Tokugawa Castle in Wakayama; he later went to Tokyo
and graduated from the college Keio Gijuku (now Keio University);
then he became a school principal, and eventually a bank director.
Takuji Ogawa received at home from his father the traditional classical education of a samurai; he also attended the Junior High School
76
Laurie M. Brown
at Wakayama, and at seventeen he went to Tokyo to study English
and to obtain a modern education. In October 1892, on a trip to
Nagoya, he witnessed the immediate aftermath of a powerful earthquake and this, together with his love for the mountains and the
seashore, helped fix his interest in geology. He became an important
man in this field and in 1901, at the age of thirty-one, he was the
youngest of the Japanese representatives who were sent to the International Exposition and Geological Conference held in Paris. He
stayed in Europe for more than a year before returning to Japan. A
few years later, on the eve of the Russo-Japanese War, he spent a year
in China as one of six scientists making a survey of mineral resources.
Yukawa stresses the catholicity and breadth of his father’s interests:
“Although my father’s field was geology and geography, he was a man
of a great many interests, which included archeology, Chinese studies,
art, swords, chess, etc. As a consequence, not only his study, but also
the storage house and the living rooms of our home literally
overflowed with books . . . Being in this kind of atmosphere, I naturally grew up to like books and to read omnivorously . . . probably it
contributed a great deal to the fact that my life has been devoted
mainly to reading, thinking, and writing.”zo
A many-sided cosmopolitanism characterized Yukawa’s father, and
even his grandfathers.21 In various essays and speeches,22 Yukawa
liked to point out that it consisted of Western science and techilology
superposed upon a Japanese culture that was itself a complex mixture
of various East Asian currents: Buddhism from India, transmitted via
China and Korea, with other Chinese elements (e.g., Confucianism),
as well as the indigenous Shinto tradition. By the twentieth century,
the result was a heady sort of creative confusion.23
Yukawa’s father was of the same sturdy generation as Hantaro
Nagaoka, Japan’s most famous physicist of the pre-quantum era.
When Nagaoka’s father returned from a trip to the West, he
apologized to his eight year old son for having “misled” him up to that
point by teaching him the wrong subjects.% Nagaoka himself, whose
work on atomic models attracted the attention of the Cambridge
school and Ernest Rutherford, and who became an authority on spectroscopy, geophysics, and other subjects, said on one occasion that
“there was no point.. . to be born a man, if I failed to enter the
advanced ranks of researchers and to contribute to the development
Yukawas’s Prediction of the Meson
77
of some field of learning.” Nagaoka was an important role model: late
in life Yukawa said that “probably the one decisive factor’’ to set him
on the path of physics’research, when he was still in high school, was
that “one could find among the Japanese ahead of one such a great
p h y s i ~ i s t . ”In
~ ~1933, when Yukawa was appointed to his first job as
Lecturer at Osaka University, Hantaro Nagaoka was its President. He
exercised little direct scientific influence on Yukawa, however; while
sympathetic to quantum mechanics, he was not able to master it in a
technical sense.
Before deciding to be a physicist, Nagaoka had hesitated:
. .wanted to know whether any Oriental had ever succeeded in research in natural
science. I wanted to be sure that any Oriental could have anything to gain by doing
research, or whether we were dependent upon Europeans.
Then he discovered that the Chinese had kept accurate records of
eclipses, and that Chinese documents 2000 years old mention meteors
and auroral phenomena:
Thus I found that in the past China was often far ahead of Europe . . . I finally decided on
a career in physics after learning about the Oriental contributions to science.25
A t the age of five or six, even before he started school, Hideki began
to study the Chinese classics with his grandfather. The method of
instruction, called sodoku, consisted of reading the Chinese characters
(kanji) aloud in Japanese pronunciation, without attending to the
meaning of the text. Yukawa says: “Each kanji held a secret world of
its own; many kanji made a line and several lines made a page. Then
that page became a frightening wall to me as a boy; it was like an
enormous mountain that one had to climb.” The beloved grsndfather
sat across the table and pointed to the kanji with a‘stick. Yukawa said,
“I was even afraid of the stick in my grandfather’s hand.” This training
was not usual in Yukawa’s day, although it had been a part of traditional samurai upbringing. Probably all of the first generation of
physicists came from samurai families and thus shared a strong
background in Chinese studies; Chinese was “the Latin of East Asia”,
the traditional vehicle of Iearned discourse.26
Yukawa remembers his mother as very kind and attentive, often
reading to the children. In the afternoons sweets were brought from a
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Laurie M. Brown
neighborhood shop. However, many innocent games and entertainments were forbidden as time-wasting. A tutor came to the house to
give instruction in calligraphy and this Hideki considered as tedious as
the sodoku.27 But the memorization of kanji turned out to have its
positive side when Yukawa began school, because he learned to read
very quickly and became an avid reader, especially of imaginative
literature.
His reading included many Japanese and Western classics, French
and German novels, as well as Turgenev, Tolstoi, and especially Dostoievski (in translation). Among the Japanese authors he mentions
Soseki, whose 1908 novel, Sanshiro, concerns a lad from the provinces
who is attending Tokyo Imperial University. At a gathering of students, one of them makes a public speech along these lines:
We, the youth, can no longer endure the oppression of the old Japan. Simultaneously, we
live in circumstances that compel us to announce to the world that we, the youth, can no
longer endure the new oppression from the West. In society, and in literature as well, the
new oppression from the West is just as painful to us, the young men of the new age, as is
the oppression of the old Japan.ZB
As a boy, Yukawa says, he showed no indication of becoming a physicist, but was deeply interested in literature. When he did become a
physicist, though, his attitudes were probably influenced by his early
reading, which was liberal and which encouraged originality.
Yukawa was shy, quiet and reticent, both as a child and throughout
his later life. Sometimes this took an extreme form, so that his public
lectures became almost inaudible. In The Traveler he contrasts his
personality with his father’s in this way: “Theoretical physics, simply
stated, is a science that tries to find the things hidden at the root of the
Universe, and is actually very close to philosophy. Geology, on the
other hand, must live closely with natural pheno’mena. Our choice of
careers shows the difference in temperament between father and
son.” On one occasion his father suggested a period of study abroad,
in which Hideki had no interest. He says, “I never felt any yearning
for foreign countries, but I never said how I felt out loud. I could not
speak in front of my father because I was afraid of him.” And in
another place he remarks, “At times the silence was itself an act of
insubordination to my father. So I was not basically timid. I began to
feel antagonistic toward Confucianism.” In fact his first grade teacher
Yukawas’s Prediction of the Meson
79
wrote of him: “has a strong ego and is firm of mind.” So his quietness
was more akin to rebellion than to timidity. In later years this personality was strong enough to reject the dicta of Niels Bohr and Werner
Heisenberg and to find a new approach to the problem of nuclear
forces.
In adolescent search for life’s meaning, Yukawa discovered the
writings of the Taoist sages Laotse, Chuangtse, and later Motse. These
authors, unlike Confucius, placed nature, not man, at the center of the
universe. “Theirs is a type of fatalistic naturalism very much like that
to which the scientific view of nature may ultimately lead.”29 Yukawa,
partly in rebellion, was thus attracted to a style of thinking that was
materialist and dialectical, but that was still very different from the
dialectical materialism of Karl Marx and Friedench Engels that
strongly influenced his first students and c o l l a b ~ r a t o r sWhen
. ~ ~ asked
about Yukawa’s philosophy recently, Mituo Taketani responded
“Well Yukawa is a genius-type, and so he has his own philosophy.”
Although philosophically inclined, and although interested in hearing
about Marxist philosophy and Taketani’s own methodology of science, Yukawa says little about the latter subjects in his essays, public
talks, and dialogues.
In 1923 Yukawa entered the Third High School of Kyoto, an institution more like a German Gymnasium or French Zycke than an
American high school. Only eight high schools then existed in all
Japan; to obtain admission as a student was difficult. His outside
reading at this time was directed toward philosophy, especially the
philosophy of science, and he read books by popularizers of science,
especially Jun I~hiwara.~‘
Einstein’s visit to Japan in 1922 (during
which he learned that he had won the Nobel Prize in Physics for 1921)
further stimulated Yukawa’s interest in physics. The visit, treated as a
great public event, impressed many of Yukawa’s *generation.
As Yukawa searched through bookstores for practice material for
his second foreign language, German (his first was English), he discovered the first volume of Max Planck’s Introduction to Theoretical
Physics. Delighted to find that he could understand both the German
and the physics, this experience helped to resolve his future career. He
took and passed the entrance examination of the Department of
Physics of Kyoto University and began his studies there in 1926.
One of his classmates at the Third High School, who also went to
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Laurie M. Brown
Kyoto University to study physics, was Sin-itiro Tomonaga, the son of
a philosophy professor at the University. In their third and final year
as undergraduates, Tomonaga and Yukawa helped each other to learn
quantum mechanics; after graduation they stayed on together for several years as unpaid “assistants” at the Physics Department. (Yukawa
says, “The Depression had made scholars.”) In 1932 Tomonaga
moved to Tokyo to join the group of Yoshio Nishina at the Institute
for Physical and Chemical Research, a private research foundation,
while Yukawa remained at Kyoto University as Lecturer of Physics.
Tomonaga shared the Nobel Prize for Physics in 1965 with Julian
Schwinger and Richard P. Feynman “for their fundamental work in
quantum electrodynamics.” In Tabi-bit0 Yukawa contrasts himself as
a stubborn person who tends “to go too far” without enough thinking,
with Tomonaga, who was more controlled: “a person aware of the
limits, who yet comes up with clever ideas.”
None of the professors at Kyoto understood quantum mechanics
well enough to lecture on it (with the possible exception of the astronomer Toshima Araki),32 but Masaji Kimura invited a young German, Otto Laporte. Then Arnold Sommerfeld, Laporte’s teacher,
came to Kyoto to lecture, followed by Paul A. M. Dirac and Werner
Heisenberg; and then there were lectures by the Japanese physicists
Bunsaku Arakatsu, Yoshikatsu Sugiura, and Yoshio Nishina, all of
whom had studied abroad. Yukawa said, “I felt as if I had been
entrusted with the task of nurturing the bud of new physics which they
had planted in me.”33
During his second year at the University (1927-28), he spent all of
his spare time in the physics library ignoring, he said, all the old books
on the shelves, but reading eagerly the recent issues of the foreign
journals, especially those in German. After “nibbling” at a variety of
papers on quantum mechanics, be began the systematic study of Erwin
Schrodinger’s papers. He realized that these papers emphasize the
continuity of nature (in the form of the wave function), in contrast to
Max Born’s Mechanics of the Aforn, read the previous year, which
stressed the discontinuity of the quantum jumps. The young scholar
saw the need for unifying these two views, a task that was soon to be
accomplished by Schrodinger and by Dirac.
In the third year Yukawa did experimental work in spectroscopy in
the laboratory of Professor Kimura, but although he found the work
Yukawas’s Prediction of the Meson
81
fascinating he elected to do a theoretical undergraduate thesis. “Desperately trying to reach the front line of physics,”18 he became afraid
that he might be too late to make a significant contribution. Still, he
noted that there remained the problem of relativistic quantum
mechanics.
A great step toward a consistent theory combining quantum
mechanics with the restricted theory of relativity, although not the
complete solution, was made by Dirac in 1928. His theory had as one
consequence the existence of states of negative energy (negative
mass),which appeared to be meaningless. Nevertheless, the theory
was highly respected for its ~ r i g i n a l i t yIt. ~was
~ on the Dirac equation
that Yukawa did his undergraduate thesis, and although he contributed nothing original to the subject in his work, it is significant that
he chose that difficult and controversial problem to study. After this
he remained at Kyoto, working in the research group of Professor
Kajuro Tamaki, as did his colleague Tomonaga. Tamaki’s special
fields of interest were classical mechanics, relativity, and musical
acoustics.
3. Beware of nuclear electrons!
In 1974 Yukawa gave a lecture in which he discussed the natural
philosophy that prevailed when he graduated from Kyoto University:
At this period the atomic nucleus was inconsistency itself, quite inexplicable. And why? because our concept of elementary particle was too narrow. There was no such word in
Japanese and we used the English word - it meant proton and electron. From somewhere
had come a divine message forbidding us to think about any other particle. To think
outside of these limits (except for the photon) was to be arrogant, not to fear the wrath of
the gods. It was because the concept that matter continues forever had been a tradition
since the times of Democritus and Epicurus. To think about creation of particles other
than photons was suspect, and there was a strong inhibition of such thoughts that was
almost unconscious.3s
In the same lecture he stressed the inadequacy of the proton-electron
nuclear model, evidenced by the notorious violation of the spin and
statistics theorem of quantum mechanics. For example, in the proton-electron model, the nitrogen-14 nucleus would contain 14 protons
and 7 electrons, or 21 fermions; yet the molecular spectrum of nit6 Centaurus XXV
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Laurie M . Brown
rogen gas showed that it behaved as though it contained an even
number of fermions. Before a satisfactory quantum mechanical model
of the nucleus could be formulated, it was essential to remove the
electrons from the nucleus. In retrospect, all nuclear theorists agree,
and Hans Bethe adds: “Regardless of the particular difficulties with
spin and statistics, it would have been impossible for anybody to do a
quantum mechanics of a nucleus composed of protons and electron~.”~~
Aside from the problem of understanding the nucleus, the other
major challenge to theoretical physics, as seen by young Yukawa, was
to make a theory of photons interacting with electrons in a relativistically self-consistent way. Heisenberg and Pauli had already attempted
to make such a quantum electrodynamic^,^^ but they discovered that
the value predicted by the theory for the electromagnetic mass of the
electron was infinite! The theory, therefore, was either not complete
or not correct, and its other predictions were accordingly put in doubt.
Yukawa likes to refer to the problem of relativistic quantum field
theory as a “settling of accounts”. By this he means that after reaping
the great rewards of quantum theory in treating non-relativistic
mechanical systems (atoms, molecules, and crystals), theoretical
physics was morally obliged to try to solve that old puzzle of the
quantum theory: the wave-particle duality of the photon.
The leading theorists of the day were prepared to accept quite
radical hypotheses in order to solve the nuclear problem. Indeed, it
seemed that at the nuclear scale of distance (the same as that at which
H. A. Lorentz had, early in the century, predicted a breakdown in
electromagnetic theory), the triumphant revolution of quantum
mechanics was about to. be repeated, and that a new fundamental
generalization of dynamics might be realized. Bohr attributed the
peculiarities of beta decay to a failure of energy donservation; Heisenberg sought to introduce a new fundamental constant, a quantum of
length to characterize the nuclear region.38
Yukawa chose a problem in spectroscopy, the inexhaustible testing
ground for quantum theory, for his first theoretical research after
graduation. He had written on Dirac’s electron theory for his senior
thesis and knew that the theory gave correctly the fine structure of
the spectral lines of hydrogen, an effect that Sommerfeld had earlier
been able to account for as a relativistic “correction” to the Bohr
Yukawas’s Prediction of the Meson
83
theory. Dirac’s theory also included the electron’s spin and magnetic
moment, and gave a correct “prediction” of the latter’s magnitude.
Yukawa’s idea was to calculate an additional very small splitting of the
atomic spectral lines, called hyperfine structure, that corresponds to
the energy difference of an electron taking one or the other of its
two allowed orientations in the magnetic field of the nucleus.
This splitting is largest for electrons that approach the nucleus most
closely, the so-called s-electrons, and these are also the “most relativistic” ones. Thus hyperfine structure tests quantum theory for
electrons near the nucleus and for large electron velocities; while it
can be handled by the methods of atomic physics, it probes at the same
time the nucleus and the relativistic unknown. Yukawa presented the
finished manuscript of his work to Professor Tamaki, who locked it in
his office safe, saying he would examine it “when he had time”. A few
months later, an article on the same subject by Enrico Fermi appeared
in Zeitschrift fur Physik.39It covered the same ground and was much
better done, as Yukawa later ruefully admitted.35
In the spring of 1931, Yoshio Nishina (1890-1951) of the Institute
of Physical and Chemical Research (IPCR) of Tokyo,40lectured on
quantum mechanics at the University of Kyoto. The lectures were
intended for the professional staff rather than students, and they consisted of an introduction to Heisenberg’s Die physikalischen Prinzipien der Quantentheorie (1 930). In the discussion period, Yukawa and
Tomonaga raised most of the questions.41
Nishina is generally regarded as the father of nuclear and cosmic ray
physics in Japan. A graduate in Electrical Engineering of Tokyo University, he joined IPCR one year after it was founded in 1917, with H.
I. H. Prince Fushimi at the head of its distinguished Board of Trustees.
After several years he was sent abroad for further study and research:
one year at the Cavendish Laboratory in Cambridge, England, one
year at Gottingen, and six years at Copenhagen with Niels Bohr,
where he wrote a famous theoretical paper with the Swedish physicist
Oskar Klein on the rate and angular distribution of Compton scattering, using Dirac’s theories of the electron and of quantum electrodynamics. Returning to Japan in 1928, he began to build the
Nishina Group at IPCR in Tokyo, primarily to do research in nuclear
physics.
The lectures at Kyoto and, perhaps to a greater extent, the social
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Laurie M. Brown
contact with Nishina, transformed Yukawa. Sakata, who was a relative
of Nishina by marriage, often visited him and was introduced on one
occasion to both Yukawa and Tomonaga when the two were having
intense discussions with Nishina on nuclear physics. “Professor Nishinayslectures were not just explanations of quantum physics”, Yukawa
said, “for he carried with him the spirit of Copenhagen, the spirit of
that leading group of theoretical physicists with Niels Bohr as its
center.” Furthermore, Nishina’s personality put Yukawa at ease; usually silent and withdrawn, he found that he could talk easily with the
older man. “My solitary mind, my closed mind, began to open in the
hands of Doctor N i ~ h i n a ” . ~ ~
The year 1932 was a turbulent one for Hideki Ogawa. In that year
he married Sumi Yukawa, took her family name, and went to live in
her family’s home in the brash, crowded, busy city of Osaka, a commercial seaport very different from his own restrained and traditional
Kyoto. He was appointed an instructor in the University of Kyoto and
asked to lecture on quantum mechanics. To the shy young man, who
still wore the short-cropped hair and the school uniform of a student,
so many changes were bound to be upsetting. Among those attending
his first lectures were Shoichi Sakata and Minoru Kobayasi, followed
the next year by Mituo Taketani. These three later became collaborators of Yukawa in the work on the meson theory that followed
the discovery of the cosmic ray meson (the muon) in 1937.
As Yukawa points out in his autobiography, 1932 was even more
turbulent for nuclear physics than it was for his personal life. That year
saw the discoveries of the neutron and the positron, as well as the
disintegration of nuclei by artificially accelerated protons (and even by
deuterons, discovered that very year).42 Yukawa became aware of the
opportunity to make a truly significant contribution to physics. For
this reason, the next two years were the most difficult, and at the same
time, the most satisfying of his life.
Before the discovery of the neutron brought about the possibility of
making a nuclear model without electrons, Yukawa was having the
same difficulty as other more mature physicists in understanding the
nucleus. He studied “what was probably the only organized book on
the theory of the nucleus at that time”,35 George Gamow’s Constitution of Atomic Nuclei and Radioactivity (1931). In Gamow’s book
many discussions dealt with properties of “nuclear electrons”, and
Yukawas’s Prediction of the Meson
85
these passages were always set off between special signs (intended to
be skull and crossbones originally) to remind the reader that the content was speculative, and possibly incorrect.
One such passage deals with the nuclear beta decay process, in
which electrons appear to emerge directly from the nucleus. (Could
there be a better proof that the nucleus contained electrons?) However, Gamow says,
These results lead us to a very strange conclusion. Since there is no process Compensating
for the difference of energy lost by different nuclei of the same element in the ejection of
a 8-particle, we must deduce, according to the principle of conservation of energy, that
the internal energy of a given nucleus can take any value within a certain continuous
range. This . . . however, has not the slightest effect before or after the &emission . . .
there is no trace of a continuous distribution of energy in the emission of a-particles or
y-rays. In these processes all the nuclei seem to be again identical.
Perhaps, Gamow concludes, “as was pointed out by N. Bohr, we must
reckon with the possibility that the continuous distribution of energy
among the nuclei is fundamentally not observable, or, in other words,
has no meaning in the description of the physical processes. . . This
would mean that the idea of energy and its conservation fails in dealing
with processes involving the emission or capture of nuclear electrons. ”43
It is important to realize that although Pauli had begun to suggest
the possible existence of a neutrino (he called it “neutron”) by the end
of 1930, he did so very cautiously and without publishing it.44 In his
“Ancient History of Beta Decay”, Yukawa says that he was unaware
of Pauli’s thinking on beta decay, but knew Bohr’s ideas. “Hastily
gathering the papers from the 1931 International Conference on
Nuclear
held in Rome, I noted quite a few papers in Italian,
but fortunately Bohr’s papers were in English: if was strange to put
electrons in something as small as the nucleus, even with quantum
mechanics, but an electron must be there. However, it may behave in
a completely different manner; even the law of conservation of energy
does not survive. . .”35
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Laurie M . Brown
4. Heisenberg’s papers on nuclear structure
Although few theorists doubted by the end of 1934 that electrons
should be strictly excluded from the nucleus,46this was far from clear
to Heisenberg when he wrote his nuclear structure papers in 1932; on
the contrary, it became the common view of physicists only after
Fermi’s publication of his theory of nuclear beta decay, according to
which electrons or positrons that come out of the nucleus are created,
together with neutrinos, as they emerge.
Iwanenko had proposed a neutron-proton nuclear model even before Heisenberg, and was also probably the first to suggest (at least in
print) that beta-decay electrons are born at their moment of emis~ i o n “Heisenberg”,
.~~
says Peierls, “took a very complicated view”,
and offers these direct quotations: “The disintegration experiments
permit us to regard. . . the neutron as an immutable elementary particle”, but “the heavy nuclei. . . includep-emitters and, on the assumption of immutable neutrons, would also have to contain electrons.”
Heisenberg’s complicated views are also attested to by Bromberg,
who discussed them personally with Heisenberg in 1970. She concluded that Heisenberg had believed “the neutron seemed to be
elementary as well as complex.” Heisenberg himself recalled
. . .we had an unclear feeling that the neutron somehow can be considered as consisting
of proton and electron, but also somehow not.48
The confusion that still surrounds Heisenberg’s papers comes from his
attempt to combine two immiscible theories. One was an essentially
correct theory (though requiring substantial modification) of nuclear
structure; the other was an essentially incorrect theory of neutron
structure. The former, in its purely phenomenological aspect, treated
the neutron as an elementary particle of spin one-half, of small
magnetic moment, obeying Fermi-Dirac statistics, etc. ; the latter, a
fundamental theory of the neutron, treated it incorrectly as a proton-electron compound.
Aside from the natural wish to account for the existence of the
neutron and the apparent need, at some level, to include electrons in
the nucleus to allow for beta decay, there were two physical effects
that seemed to require a composite neutron. One was the “anomalous
absorption” of hard gamma rays, while the other had to do with
Yukawas’s Prediction of ihe Meson
87
cosmic ray electrons. The processes are mentioned by Heisenberg at
the end of his first paper on nuclear structure, where he says that his
theory does not hold for them:
Such phenomena are the Meitner-Hupfeld effect, the scattering of y-rays on nuclei;
further all experiments which split neutrons into protons and electrons (an example is the
stopping of cosmic ray electrons on their passage through nuclei). For the discussion of
such experiments we have to investigate more precisely all the fundamental difficulties
that appear in the continuous &ray spectra.49
These effects are discussed in Parts I1 and I11 in terms of a composite
neutron, and one even finds the statement in Part I11 that alpha particles must be made, not ofprotons and neutrons, but of protons and
electrons, in order that they have the large polarizability required to
explain the gamma ray p h e n ~ m e n aIn
. ~fact,
~ the high energy processes mentioned turned out to involve electromagnetic shower or cascade processes: photons converting into electron-positron pairs, subsequent annihilation of the positrons producing photons, and electron
and positron deflection, likewise producing photons (Bremsstrahlung). These are all electromagnetic processes and in no way related to
the continuous P-ray spectrum. We turn, therefore to the part of
Heisenberg’s work that concerns nuclear structure, the part generally
conceded to have had lasting value.
Heisenberg sets out an admirable program: “to discuss the consequences of the assumption that atomic nuclei are built out of proi.e.,
tons and neutrons without the collaboration of electron~”,5~
“loo~e”electrons, not bound in neutrons. This reduces the B-decay
problem to the question of how the neutron in the nucleus decays into
proton and electron; the nitrogen statistics problem becomes that of
the statistics of the neutron; and most important of all, the structure of
the nucleus itself is described by quantum mechanics in terms of the
interaction forces between heavy (thus non-relativistic) nuclear particles.
Heisenberg inferred from experiment that the neutron has spin ‘I&
and that it obeys Fermi-Dirac statistics. These are properties of the
proton as well, so that: “To interpret the neutron as composed of a
proton and electron, one would have to ascribe to the electron Bose
statistics and spin zero. However, it does not seem useful (zweckmassig) to consider this picture more closely.” Rather, “the neutron
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Laurie M. Brown
should be considered an independent fundamental particle that can,
under appropriate circumstances, split into a proton and electron,
whereby presumably the conservation laws of energy and momentum
are no longer applicable.” The violation of these last conservation
laws does not follow from Heisenberg’s picture, but is assumed in
order to fit the @-decay observations, while angular momentum conservation and the spin-statistics theorem necessarily fail.
To build a quantum mechanical model of the nucleus, analogous to
those for the atom, the molecule, and the crystal, Heisenberg constructs the Hamiltonian function of the nucleus, formulated as the sum
of kinetic energy terms for each proton and neutron and interaction
energies for each nucleon pair, but without electron coordinates appearing explicitly.
At this point, as a pure hypothesis, Heisenberg introduces a series
of analogies drawn from molecular physics that result in his famous
charge-exchange force. The strongest interaction, by analogy with the
H,+-ion, is supposed to be that between proton and neutron. In one
picture of the H,+-ion (which consists of two protons and an electron),
the electron was associated in a quasi-atomic state, with one or the
other proton alternately. In Heisenberg’s nuclear model, the analogue
of that quasi-atomic state is the neutron, viewed as a closely bound
state of a spinless electron obeying Bose statistics. However, he uses
the resulting phenomenological form of the exchange force “without
reducing it to electronic motions.”
The composite picture of the neutron leads to the introduction of an
additional neutron-neutron force in analogy to the force in the neutral
hydrogen molecule, where two protons share a pair of electrons. As in
the molecular analogy, the neutron-neutron force is weaker than that
between proton and neutron. Both of these nuclear exchange forces
are expected to vanish beyond some distance ‘like lo-” cm. Since
Heisenberg considers the proton fundamentally simple, he assumes
only the basic Coulomb repulsion to act between protons. Finally, in
order to complete the energy balance he adds a term to the Hamiltonian function to account for the mass difference between neutron
and proton.
The Hamiltonian finally written by Heisenberg depends only upon
the coordinates of the protons and neutrons, consisting of the usual
space and spin coordinates and a new fifth one, e, to distinguish the
Yukawas’s Prediction of the Meson
89
character “neutron” (with e = +1) from “proton” (with e = -1).
Formally introducing a new space (later called “charge space”) and a
2 X 2 formalism analogous to Pauli’s spin matrices, Heisenberg’s
Q -coordinate is the forerunner of the isospin formalism, prominent in
modern nuclear and elementary particle
In Heisenberg’s
nuclear structure papers, the new labels for proton and neutron are
convenient for writing interaction terms that transform one of the
nucleons into the other, but their use does not provide any new
dynamical insight and is not necessary; Majorana, for example preferred to ignore these labels when he extended Heisenberg’s
Having written down a Hamiltonian function with five sets of terms
(kinetic energies, proton-neutron exchange J, neutron-neutron exchange K , proton-proton Coulomb energy, and mass difference
terms4), Heisenberg claims that the problem of nuclear structure has
been reduced to a purely mathematical one, that of drawing out the
content of the Hamiltonian function.
Even without detailed calculation, a rough qualitative picture of
nuclear systematics emerges. The largest terms of the Hamiltonian,
the kinetic energy and the charge-exchange J, are symmetric in neutrons and protons. Considering these terms alone, one would conclude
that having equal numbers of neutrons and protons would be energetically favored, and would thus lead to greatest stability. On the
other hand, the long-range repulsive Coulomb force between protons
and the short-range weak attraction between neutrons both favor increasing numbers of neutrons for the stability of heavier nuclei, in
accord with observation.
Heisenberg applied his Hamiltonian function to write a Schrodinger
equation to describe the nucleus of recently discovered deuterium, the
deuteron. This contains one proton and one neutron and so resembles,
in essentials, the two-electron problem of atomic physics, typified by
the helium atom. The normal state of the deuteron, that of lowest
energy, has neutron and proton in the same orbital state, i.e., it is
symmetric in the exchange of positions of the two nucleons. The spin
function of the two nucleons can be either symmetric (spin one) or
antisymmetric (spin zero), while the wave function, similarly, can be
either symmetric or antisymmetric in the exchange of neutron-proton
character (@-coordinate). If the interaction potential J is chosen to
have the same sign as it has in the hydrogen-molecular ion, then the
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Laurie M . Brown
deuteron spin must be zero, by extension of Pauli’s exclusion principle
to the nucleus. This prediction is false (though Heisenberg did not
know it at the time), necessitating a choice of the opposite sign for J.55
Heisenberg continues in Part I to show that the helium nucleus has
“closed shells” of both protons and neutrons, and should thus be
particularly stable. Structures containing only neutrons would be
bound (by the attractive neutron-neutron force K ) , but not so strongly
as structures having the same number of nucleons (i.e., isobars), some
of them being protons. Thus the beta-decay process occurs in nuclei
that are too “neutron-rich”, a neutron becoming a proton plus an
electron. (Heisenberg does not accept Pauli’s neutrino at this stage.)
As the positron had not been discovered at the time of Part I, he does
not discuss the possibility of positron decay of “proton-rich” isotopes.
Indeed, Heisenberg’s theory, in which the proton is not composite,
provides no mechanism for it.
Part I1 of Heisenberg’s paper was sent from Ann Arbor, Michigan,
in July of 1932, still before the positron discovery was announced in
August. Again, his purpose is to determine “to what extent the fundamental difficulties in the theory of the nucleus can be reduced to the
questions concerning the existence and properties of the neutron.” He
points out that the stability of the neutron in scattering, together with
its size, implies a very large binding energy of electron to proton, “of
the order of 137 mc2 [mis the electron mass], while the observed mass
defect is about one hundred times smaller.”56 He concludes that the
very existence of the neutron (as an electron-proton compound) contradicts quantum mechanics and so, making a virtue of necessity, argues that there is nothing wrong with considering it as a “fixed
elementary particle in the nucleus.’’
Part 111 reveals a new problem: Heisenberg’s charge-exchange force
and/or an ordinary (non-exchange) neutron-proton force do not produce saturation. In other words, the model nucleus collapses with
increase in particle number, and the binding energy increases proportional to the square of the number of nucleons, rather than linearly, as
observed. Heisenberg reaches this conclusion from a statistical treatment of the nucleus (Fermi-Thomas model). His remedy is to introduce a repulsive core at short distances to the two-nucleon interaction
potential.
Ordinary (i.e., non-exchange) forces between neutron and proton
Yukawas’s Prediction of the Meson
91
were considered about the same time by Eugene Wigner, who also
neglected the forces between like particles in the very light nuclei.57
Wigner explained that the very large binding energy per particle of the
helium nucleus could be reconciled with the much smaller binding
energy of the deuteron providing the nuclear potential well is taken to
be deep, but narrow. The deuteron is weakly bound because its wave
function spreads mostly outside of the well, while the wave function of
the helium nucleus is “pulled in” by the larger number of attractive
bonds, so that its nucleons spend a longer time, on the average, in the
deep attractive well; this increases the binding energy per nucleon
pair.
Majorana’s modification of Heisenberg’s Hamiltonian also deserves
mention. Abandoning the latter’s atomic physics analogies, Majorana
considers a specific nuclear strong interaction force between elementary neutron and elementary proton, ignoring like-particle forces for
the light nuclei. This force is chosen to produce a constant nuclear
density, i.e., saturation, ruling out both ordinary and charge-exchange
forces if only one kind of nuclear force is assumed. Majorana proposes
a force of space-exchange character, but spin-independent, so that in
the strongly bound helium nucleus both neutrons are attracted equally
by each proton. (Heisenberg’s charge exchange force is equivalent to a
combined space and spin exchange.) Majorana’s exchange force produces saturation without the need for introducing a repulsive interaction core.53Eventually, however, both the spin-independence and the
dominance of neutron-proton force had to be dropped.
5. Fermi’s theory of beta decay
Heisenberg initiated the study of a nuclear model having protons and
neutrons interacting in pairs according to nor-relativistic quantum
mechanics. He assumed the validity of the usual conservation laws in
determining nuclear structure, but nevertheless denied their applicability to the structure of the neutron itself, o r to processes, like beta
decay, that seemed to be related to the neutron’s structure. Thus in
spite of the supposed analogy with molecular exchange forces, the
strong nuclear forces introduced by Heisenberg (and Wigner, and
Majorana) must be considered only phenomenological.
On the basis of strong forces of short range, and perhaps a repulsive
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Laurie
M. Brown
core interaction to achieve saturation, a reasonable picture of the
nucleus emerged, yielding at least qualitative understanding of the
tendency for nucleons to cluster into alpha particles within the nucleus, the nuclear energy level spectrum, and elastic and inelastic
scattering by the nucleus of projectiles such as protons, neutrons, and
alphas. No important conceptual problems remained with alpha and
gamma radioactivity, but without introducing the neutrino (or its
equivalent), it was impossible to construct a consistent theory of beta
decay on the basis of any known form of quantum mechanics, relativistic or not. As long as beta decay was regarded as a process in
which a single electron or positron emerged from the nucleus with a
variable amount of energy, while the nucleus made a transition between definite quantum states, it was impossible to maintain the conservation of energy and momentum.
Nevertheless Heisenberg, like Bohr and others, rejected the neutrino; he failed even to mention it! Before admitting the possible existence of a new substance, a new elementary particle, he was willing to
abandon even the hard-won conservation laws, considered by most
physicists to be the very pillars of physical science. Bohr and Heisenberg, indeed, seemed to welcome the apparent failure of quantum
mechanics, relativity, electrodynamics (and what else?) at nuclear dimensions, and hoped that it might lead to new conceptions of space,
time, and causality - possibly to a new unification of natural
philosophy.
While some who had made the modern quantum theory were
plotting a second revolution, Enrico Fermi made a “tentative theory
of beta rays” that conserved all the important dynamical quantities
through the simultaneous creation and emission of a neutrino together
with the beta decay e l e ~ t r o n .His
~ , ~theory
~
complemented Heisenberg’s nuclear model; using both, the nucleus could be regarded as an
entirely quantum mechanical system. Fermi assumed the existence of
Pauli’s neutrino and allowed only protons and neutrons in the nucleus.
Consequently electrons and neutrinos must be created when emitted;
in this respect they resemble the photons emitted by an excited atom
or nucleus.
A typical beta process involves the decay of a neutron into a proton
plus electron plus neutrino. Fermi does not treat the decay of a free
neutron, but of one bound in a nucleus. In order for a free neutron to
Yukawas’s Prediction of the Meson
93
decay, it must be more massive than a proton plus an electron, but at
the time that Fermi wrote his paper it was not even known that the
neutron was heavier than the proton
On the other hand, for a
neutron bound in a nucleus, and therefore interacting with the other
nucleons, the source of the decay energy is the difference of mass
between the parent and the daughter nucleus, of which the neutronproton mass difference is only a part. (For the same reason, mutatis
murandis, the proton in a proton-rich nucleus can decay into a neutron
plus a positron plus a neutrino, even though thefree proton is lighter
than the free neutron.)
The fundamental process of beta decay is thus described by Fermi
as one in which a neutron in the nucleus transforms into a proton, with
the simultaneous emission of an electron and a neutrino. In the reverse process, a proton transforms into a neutron upon the absorption
of an electron and a neutrino.60 The heavy particles, proton and
neutron, are characterized by Heisenberg’s e- coordinate and treated
as different charge states of a single nucleon. As in Heisenberg’s nuclear model, the heavy particles are constant in number and are described by non-relativistic wave functions.
On the other hand, to deal with the variable number of light particles, it is necessary to use the method of quantum field theory which,
especially when it is used to describe spin 1/2 particles like electrons
and neutrinos, is often called “second quantization”.61 This procedure
is analogous to the quantization of the classical Maxwell electromagnetic field that allows it to be represented by a collection of
identical elementary particles , the photons. However, in the case of
electrons, say, the “field” that is to be quantized is not really a classical field, but is the Dirac wave function that represents thefirst quantization. (Hence the name “second quantization”.) For the p-decay
electrons and the neutrinos, both the wave function theory and its
second quantized version must be relativistic. The field theory must
lead to the Pauli exclusion principle for the Dirac particles - not to the
symmetric (Bose-Einstein) statistics that light quanta obey.
It is curious that Fermi insists that his theory has no analogy to the
creation or disappearance of an electron-positron pair in Dirac’s hole
theory, since (he argues) the latter processes can be interpreted “simply as a quantum jump of an electron between a state with negative
energy and a state with positive energy with conservation of the total
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Laurie M. Brown
(infinitely large) number of electrons.’’ It is possible that Fermi was
trying to draw a sharp distinction between his theory and that of Beck
and Sitte62, which did make use of Dirac’s hole theory but implied a
violation of energy conservation, since it assumed no neutrino. But the
explanation may be simply that Fermi was not willing to regard electron and neutrino (unlike the case of proton and neutron) as different
charge states of a single particle. He could have regarded electron-neutrino creation as the promotion of a negative energy neutral
neutrino to a positive energy negatively charged electron, leaving behind a neutral antineutrino (hole in the neutrino “sea”). He does not
mention the antineutrino (although it is implicit in his theory) or
neutrino holes, which Gian Carlo Wick introduced in applying Fermi’s
theory to positron emission.63
The mathematics of Fermi’s theory rests on a Hamiltonian consisting of the sum of kinetic energy terms for the heavy and light particles
and terms describing their mutual interaction. The latter contain the
operator Q, which transforms a proton into a neutron (raising
operator) and Q*, its hermitian conjugate, which transforms a neutron
into a proton (lowering operator). They also contain the field
operators which either create an electron at the position x , namely
v * ( x ) , or a neutrino at the same position, q * ( x ) , or destroy, respectively, electron and neutrino, namely q ( x ) and q ( x ) . The interaction
part of the Hamiltonian reads,
where the Fermi constant g is analogous to the electric charge which
determines the strength of the photon interaction, or in other words,
the probability of photon emission.
The operators V ( x ) and q ( x ) , and also v * ( x ) ahd q * ( x ) , each have
four components with the same relativistic transformation properties
as a Dirac wave function, although they are not wave functions but
field operators, responsible for creating and annihilating particles.
They are analogous to the field operators in quantum electrodynamics
that give the emission and the absorption of photons. Fermi recognized that his Hamiltonian function was not unique, and that various
combinations of the field components of electron and neutrino would
allow the interaction Hamiltonian H to be Lorentz invariant. Subject
Yukawas’s Prediction of the Meson
95
to possible later modification, Fermi chose those particular bilinear
combinations of the components of q ( x ) and cp(x) which transform as
Lorentz four-vector, like the electromagnetic four-potential. By
putting these bilinears into the heavy particle Hamiltonian, where
normally the electromagnetic four-potential would appear instead, he
obtained a familiar looking Lorentz-covariant interaction.
Since beta-decay half-lives are very long on the atomic scale, Fermi
knew that the constant g is small, and applied the perturbation theory
to calculate the half-lives and the decay-electron spectra of radioactive elements.@ He showed how the shapes of the latter depend, at
their ,high energy endpoints, upon the mass of the neutrino, and deduced that the value of that mass was most likely zero.
6. From neutron to meson; Japanese physics in the early 1930’s
Let us return to Yukawa in 1932 - recently married, an Instructor at
Kyoto University, and full of doubts, both personal and scientific.
Only a few days after his marriage in April, he was scheduled to begin
lecturing on quantum mechanics; there was not enough time for a
honeymoon, and the bridal pair settled for a day trip to the seashore.
Some of the students that heard his Kyoto lectures were to become
his scientific collaborators a few years later, but the lectures that
caused so much anxiety to Yukawa did not make any great impression
on them. In Tabi-bito, Taketani is quoted:
There were no particular characteristics to Mr. Yukawa’s lectures, which followed Dirac’s textbook for the most part. His voice was gentle as a lullaby and he spoke with little
emphasis - it was ideal as an invitation to sleep.
Kobayasi added that the lectures were delivered with his back to the
audience, as he addressed the blackboard.
Yukawa lived with his wife’s family in Osaka and commuted by
train. In the new environment of the Osaka house (and out of his
father’s shadow), some changes began to take place in Yukawa’s personality, although he still found it difficult to break his “life-long habit
of silence”. He admits, “I never spoke with my adopted parents unless
absolutely necessav..” His father-in-law, a retired physician, was an
96
Laurie
M.Brown
Orientalist who collected art objects and required his family to study
Japanese dance, tea ceremony, and other arts. The atmosphere was
old-fashioned, and for Yukawa “easy to accept .,. It gave relief to the
tired and strained mind.”1s His marriage, his new job, and his new
home in busy Osaka, all conspired to his awakening - but equally so
the new physics of 1932.
After the neutron discovery, when Heisenberg’s papers on nuclear
structure arrived in Japan, Yukawa’s interest in nuclear physics quickened. Shoichi Sakata, then a.third year student at Kyoto, recalls that
Yukawa advised him to write his bachelor’s thesis on that subject.41
Yukawa translated Heisenberg’s papers and wrote a perceptive introductory essay, his first p ~ b l i c a t i o n It
. ~ shows
~
his recognition of the
phenomenological nature of Heisenberg’s theory and the need for a
better fundamental mechanism. Very soon after this, Yukawa presented his first paper at a meeting of the Physico-Mathematical Society of Japan, held at Sendai in April of 1933, on the “Theory of
Nuclear electron^."^^
Tomonaga, during a symposium held in 1961, recalled Yukawa at
the Sendai Meeting, sitting on the ground and writing equations in the
dirt of the exercise field of Tohoku University, trying to relate the
nuclear force to thep-decay process. Tomonaga: “He was saying that
the nuclear force is all right [in Heisenberg’s theory] but in @ decay a
strange particle ernerge~.”6~
Yukawa was trying to understand @ decay
and nuclear forces on the basis of Heisenberg’s electron exchange. In
a later interview, Yukawa discussed his unsuccessful attempt to make
an “electron field” theory of nuclear forces, saying that Nishina had
suggested an electron with Bose statistics but, of course, no such electron had ever been detected.68
“By taking up these difficult problems,” Yukawa says in Tubi-bito,
“I had to expect long days of suffering.” He was ‘troubled with insomnia. When his father suggested that he might go abroad for study, he
rejected the proposal: “I did not want to go to foreign countries until I
had finished a work I could call my own. I would find my own theme
and pursue it as far as I could, not caring how many times I might fail.
If I succeeded, then I would talk with foreign scientist^."^^
During the 1933 Sendai meeting, Yukawa’s brother introduced him
to a colleague at Tohoku University, a well-known Professor of Electrical Engineering, Hidetsugu Yagi, who had just become Head of the
Yukawas’s Prediction of the Meson
97
physics department in the new Science Faculty of Osaka University.
Offered a lectureship, Yukawa accepted and during the next year
divided his time between Kyoto and Osaka Universities. In April,
1934 he moved into the new physics building in downtown Osaka as
full-time Lecturer and head of the “Yukawa Group”. In the same
month Seishi Kikuchi came from Tokyo Riken as Professor, and
Sakata, who had been working in Tokyo with Tomonaga, came and
shared an office with Yukawa. His impression was favorable:
Dr. Yukawa looked much more lively and active than the year before when I was taking
his course in Kyoto. Apparently he was influenced by the fresh atmosphere in the
University, generated by the presence of a number of young and active research colleagues. But it must also have been due to the environment of busy Osaka; all day we felt
the office vibrate because of the passing trucks. Yukawa used to say that he always felt
the urge to do something there.41
According to Professor Koji HusimP9, who joined Kikuchi’s research
group in 1934 after graduating from Tokyo University, it was customary for the Kikuchi and the Yukawa groups to have lunch together
every day. When Husimi came to Osaka he brought with him issues of
the Italian journal “La Ricerca Scientifica”, not available in Osaka or
Kyoto, containing Majorana’s paper on nuclear forces (also published
in Germans3), and most importantly, Fermi’s paper on beta decay4.
These were discussed at lunch (as were all sorts of questions, including
politics).
Yukawa himself said that he first came upon Fermi’s paper in the
Zeitschrift f i r Physik version35, later in 1934. And in Tabi-bit0 he
says, “I must have paled as I read it. Had I been beaten by Fermi for a
second time?” For the grasped immediately that the electron-neutrino
pair could provide a nuclear force that would be free of the contradictory aspect of mere electron exchange, and could preserve the
conservation laws even in nuclear beta decay. Very shortly afterwards, when it was shown that the force of electron and neutrino
exchange was far too weak, Yukawa recalled another idea that had
earlier kept coming briefly into his consciousness, only to be suppressed. Now, with eyes fully open, he said, “Let me not look for the
quantum of the nuclear force field among the known particles - including the new neutrino. If I pursue the characteristics of the nuclear
force field, then the nature of the quantum of that field must also
become apparent. Thinking in this manner, I was almost there.”ls
7
Ccnraurur XXV
98
Laurie M. Brown
One night in October 1934, shortly after his wife had given birth to
their second child, unable to sleep, Yukawa suddenly saw that the
range of the nuclear force must be inversely proportional to the mass
of its field quantum, and that there must be a new particle. In the
morning he found the mass to be about 200 electron masses, and
concluded that it should appear both positively and negatively
charged. At the lunch with the Kikuchi group, he reported his results.
(This is recalled also by Husimi.) Kikuchi remarked that this particle
should be visible in the Wilson cloud chamber; Yukawa agreed - and
argued that it should be found in cosmic rays. Not long afterwards the
theory was given at the Osaka branch meeting of the PhysicoMathematical Society of Japan, and presented a month later at the
Tokyo Imperial University.
Before analyzing Yukawa’s theory of the nuclear force I want to
place him more accurately in the Japanese physics milieu. I shall not
try to be complete, in part because Japanese historians have already
covered some of the
but also because, except for some
letters and unpublished reminiscences referred to below, my access to
institutional sources has been limited.
As regards the beginnings of sorymhiron (Le., nuclear and elementary particle physics) the most important institutions have been mentioned, namely, the Inperial Universities of Tokyo, Kyoto, Tohoku,
and Osaka, and the Institute of Physical and Chemical Research in
Tokyo, the Riken. In fact practically all prewar-nuclear and cosmic ray
research was done at the “new” University of Osaka, at Kyoto, and at
Riken. In Sakata’s opinion, the reason was this:
An unfortunate circumstance in Japanese science was. . . that the centers of research
were concentrated in the Imperial Universities, so that the abuse of bureaucracy hindered the free development of science in various ways. Nuclear physics, however, being a
newly born scientific field was fortunate in having begun its life (in Japan) at the only
large non-governmental research institute in the country, the Institute of Physical and
Chemical Research, and to having always advanced with this Institute at its core.’l
Recall that it was Riken that sent Yoshio Nishina abroad for what
turned out to be eight years of study and research, and that it was
Riken to which he returned in December 1928. Everyone agrees that
Nishina became the father of both nuclear and cosmic ray research in
Japan. After a period of cultural readaptation, marriage, etc., Nishina
Yukawas’s Prediction of the Meson
99
established his laboratory at Riken in July 1931, and began work
immediately on nuclear i n ~ t r u m e n t a t i o nRyokichi
.~~
Sagane, the son
of Nagaoka, had just joined the group and was designing
Geiger-Muller counters. Masa Takeuchi, hired originally to help
Nishina with x-ray analysis (an old Copenhagen interest), was told to
assist Sagane with cosmic ray research. A large cloud chamber was
built and operated in a vertical plane with a strong uniform horizontal
magnetic field, so that the curved tracks of cosmic ray particles could
be photographed and identified. Through 1932 Sagane tried to use
coincident signals from charged cosmic rays passing through electronic
counters (G.-M. tubes) placed above and below the cloud chamber, to
actuate the chamber’s expansion.73 This did not succeed, but in March
1933, P. M. S . Blackett and G. P. S . Occhialini in England reported
observing cosmic ray shower phenomenon in their counter-controlled
cloud chamber.
A second cosmic ray group used counters to measure total ionization. They made comparative measurements at sea level, at mountain
altitudes, and in a deep railroad tunnel (the Shimizu Tunnel, at 8(YO
meters of water equivalent depth), continuing this type of observation
well into the War. In 1935 Nishina wrote to Robert A. Millikan requesting aid in either the construction or the purchase of a “vibration-free, self-recording electrometer” of Millikan-Neher type (H.
Victor Neher), in order “to carry out the survey of cosmic-ray intensities in Japan.” The instrument was built in Pasadena, and arrived in
Tokyo in June of 1936.
Several small groups did nuclear physics research at Riken, using
natural radioactive sources. The Nishikawa Group studied proton and
deuteron induced nuclear reactions, using a high voltage source (Cockroft-Walton machine) in 1934; the Nishina Group began the construction of a small, and then a large (60 inch) cyclotron; slow neutron
work, inspired by the success of the Rome group of Fermi, began in
1937.
Sin-itiro Tomonaga left Kyoto in 1932 to work at the theoretical
group of the Nishina Laboratory, and was joined later by Kobayasi,
Sakata, and H. Tamaki.76 The first five papers of Tomonaga use Dirac’s positron theory and deal with the creation and annihilation of
electron pairs. All include the name of Nishina, as well as other collaborators, and are written in English. The sixth paper (1936) is on the
74775
100
Laurie M. Brown
interaction of neutron and proton. From 1937 to 1939 Tomonaga was
in Leipzig with Heisenberg; he continued his work on nuclear forces,
and published in German at that time.77
Osaka University founded its Science Faculty and began its lectures
in physics in 1933. Yagi was appointed by President Nagaoka as Head
of the Physics Department and hired new professors, S . Tomochika
from Tokyo Imperial University, and J. Asada and T. Okaya from the
Shiomi Institute for Physical and Chemical Research in Osaka.7a A
fifth position went to Seishi Kikuchi, who came from the Tokyo Riken
in April 1934 and began the construction of a Cockroft-Walton accelerator and other equipment for nuclear physics research. Born in
1902, the son of a noted mathematician and seismologist, Seishi
Kikuchi did pioneering work in electron diffraction in the late 192O’s,
for which he was awarded the Academic Prize in 1931. His nuclear
physics group at Osaka was second only to Nishina’s in Tokyo, and it
was with this group that Yukawa and his students worked, although
officially they “belonged” to Professor Okaya. The theory group
worked on problems of interest to the experimentalists and used the
latter as a sounding board. Thus it was that the first presentation of the
meson theory was made to the Kikuchi group. Sakata says that
“Kikuchi brought the free atmosphere of Riken to Osaka University,”
and the generally active and youthful spirit of the group encouraged
Yukawa’s speculative mood.79
Comparison may be in *order with Italy where revitalization of a
tradition in decline was brought about through the theoretical work of
Fermi and Majorana in Rome, by the work of Fermi’s nuclear group in
Rome, and by the cosmic ray group of Bruno Rossi in Florence. It is
tempting to imagine that Nagaoka in Tokyo and Orso Mario Corbini
in Rome played analogous roles as politicians and elder statesmen.*O
7. Yukawa predicts the meson
As we have seen, Yukawa’s thoughts had been filled for several years
with the problem of the nature of the nuclear force field; it was a
continuous preoccupation, and it appeared to him later that he had
glimpsed the solution repeatedly without arriving at a definite formulation of it. When he did grasp the essential relation between the
Yukawas’s Prediction of the Meson
101
quantum mass and force range and sat down in October 1934 to do
the necessary mathematics and to write his article, it took barely a
month for him to complete the work. It contains several new and
valuable ideas, and its physical logic proceeds inexorably.
Later physicists (until again quite recently) found little reason to
assume any unifying relation between the strong and the weak nuclear
interactions, but it was a temptation for physicists of the 1930’s. Only
for a year or two had they even considered a specific nuclear force,
unrelated to electricity and magnetism; naturally, one new force was
preferable to two. Furthermore, Heisenberg had proposed a nuclear
charge-exchange force, arising from the transfer of a spinless electron
obeying Bose-Einstein statistics. That is not the description of a real
electron, but it is a possible metaphor for an electron-neutrino pair.
It may have been Heisenberg who first suggested a connection between exchange forces and what became known as the “Fermi field”,
the latter an analogue of the electromagnetic field, with the electron-neutrino pair substituting for the photon.B1 In letters to Nature
shortly.after the appearance of Fermi’s @-decaytheory, Tamm and
Iwanenko estimated the effective potential arising from the exchange
of a pair of light particles. They found dependence upon the distance
as the inverse fifth power, when the distance is small. However, the
resulting force was too weak to provide the neutron-proton binding
force, falling short by a factor of at least 1010.82
In view of this result Yukawa said, “it seems natural to modify the
theory of Heisenberg and Fermi . . .”, and he suggested:
The transition of a heavy particle from neutron state to proton state is not always
accompanied by the emission of light particles, i.e., a neutrino and an electron, but the
energy liberated by the transition is taken up sometimes by another heavy particle, which
in turn will be transformed from proton state into neutro? state. If the probability of
occurrence of the latter process is much larger than that of the former, the interaction
between the neutron and the proton will be much larger than in the case of Fermi,
whereas the probability of emission of light particles is not affected e~sentially.8~
Yukawa states here that the interactions of Fermi and Heisenberg are
different, that they give alternative ways for a neutron to become a
proton (or the reverse): either an electron-neutrino pair is emitted
(Fermi process), or the energy and negative electric charge are taken
up directly by another proton in the nucleus, which thereby becomes a
102
Laurie
M. Brown
neutron (Heisenberg process). The first occurs with small probability
(Le., it is a weak interaction); the second has a probability large
enough to provide the binding of nucleons in the nucleus (i.e., it is a
strong interaction).
Up to this point, little has been accomplished but a modest step
backward, disassociating B decay from nuclear binding forces, but
forward progress follows immediately:
Now such interaction between the elementary particles can be described by means of a
field of force, just as the interaction between the charged particles is described by the
electromagnetic field. The above considerations show that the interaction of heavy particles with this field is much larger than that of light particles with it.
Attention has been focused upon a new field of force, which like
gravitation and electromagnetism is universal, interacting with both
heavy and light particles, but with very different strengths. The final
step in the reasoning leading to the meson theory is contained in the
next paragraph:
In the quantum theory this field should be accompanied by a new sort of quantum, just as
the electromagnetic field is accompanied by the photon.
The parallel with electromagnetism is now exploited, the force between neutron and proton being expressed first in terms of a static
potential, “in analogy with the scalar potential of the electromagnetic
field” that gives rise to the Coulomb force. “The potential of force
between the neutron and the proton should, however, not be of
Coulomb type, but decrease more rapidly with distance. It can be
expressed, for example, by
k g 2 exp (-Ar)/r
‘
where g is a constant with the dimension of electric charge.. .,,. The
second constant that appears in this generalization of the Coulomb
potential is A, having the dimensions of an inverse length, whose value
determines how the potential falls off with the distance r. The reciprocal of A is identified with the range of the potential, for the potential
falls off very rapidly at distances greater than l / A . By choosingA to be
about 1013cm-’, one obtains the nuclear force range of about
Yukowas’s Prediction of the Meson
103
cm. On the other hand, if I is allowed to become very small, the range
of Yukawa’s potential becomes infinite, the exponential becomes
unity, and the potential becomes +g2/r, the familiar Coulomb potential.
Yukawa pursues the electromagnetic parallel. The potential above
is a static one; in general, it can be time-dependent. Furthermore, the
usual electric and magnetic fields are not derived from a scalar potential alone; there is a vector potential as well, which forms a relativistic
four-vector together with the scalar potential.84 The source of the
electromagnetic four-potential (which usually appears on the
right-hand side of the wave equation) is the charge-current density
four-vector; Yukawa needs to write the analogue of this source. Finally, up to this point the theory has been classical; when it is quantized, one gets the quanta of the nuclear field, the analogue of
photons, the mesons.
I consider these steps of generalization, beginning with the wave
equation for the scalar potential. If Y(x,y, z, t ) is the electromagnetic
scalar potential, it satisfies, in the absence of sources, the wave equation
1 a2
(A2- - -)
c2 at2
V(x, y, z, t ) = 0.
In addition to time-depenilent solutions, the equation possesses the
static centrally symmetric solution: V = constant times l/r. The
generalized wave equation for Yukawa’s U-field (his “scalar potential”), is
it possesses as solution the static Yukawa potential given above, in
addition to time-dependent solutions;85 for A = 0, the equation for U
becomes that for V.
With regard to the analogue of the vector potential of the electromagnetic field, Yukawa says “we disregard it for the moment, as
there is no correct relativistic theory for the heavy particles”. (The
Dirac theory, e.g., would not be considered appropriate, as the neut-
104
Laurie M . Brown
ron and proton have anomalous magnetic moments.)86 Within nuclei,
nucleons move with an average speed about one-tenth that of light, so
that relativistic effects are not entirely negligible; but the description
used by Yukawa, representing the nucleons by simple non-relativistic
Schrodinger wave functions, is a very reasonable first approximation.
In the same spirit, the vector part of the nuclear interaction, which has
both a velocity-dependent source term and gives a velocity-dependent
interaction, is ignored.
Aside from the way that it depends upon distance, Yukawa’s new
field also differs from electromagnetism in that its “source” is the
transition from neutron to proton (or vice versa); thus the field itself
must carry electric charge (while the electromagnetic field, of course,
is neutral). From the canonical theory of fields, it follows that a field
carrying electrical charge must be complex.87
To build the charge-exchange character into the source of the
U-field, Yukawa uses Heisenberg’s @-coordinate (see Sec. 4) and the
2 x 2 matrices which act upon that coordinate.88 As the analogue of
Pauli operators which flip the spin, Heisenberg has the operator t + to
transform a proton state to a neutron state and t- to perform the
inverse process. The source of Yukawa’s U-field (carrying negative
electric charge) is the neutron-to-proton transition, given by g dt-g!~,
where 1/1 ,the wave function of the heavy particles (proton or neutron)
is a function of space, time, and spin, as well as of z3(Yukawa’s name
for Heisenberg’s ~-paramt?ter).*~
Similarly, the source of the field U
(the complex conjugate of U ) , carrying positive charge, is g
These source terms appear in the wave equations for U and U ,
analogous to the electric charge density in the wave equation for the
electromagnetic scalar potential.
Next he writes a one-particle Schrodinger equation for the nucleon,
neglecting spin. The potential function isg(Ut+ + Or-); the first term
corresponds to a proton absorbing the U-field and becoming a neutron; the second corresponds to the transition of a neutron to a proton. If U and 0 are the static central potentials that have as their
sources other protons and neutrons, moving relatively slowly, then U
and 0 are given, respectively, by ( g / r ) t 4 exp (At-),
where r is the
distance to the source, and t: and t L are the “raising” and “lowering”
operators that act upon the source nucleon.
Inserting these static solutions, Yukawa obtains the symmetric
$t+w.
Yukawas’s Prediction of the Meson
105
Hamiltonian function for a pair of interacting non-relativistic nucleons:
H
= (p32M)+(p22/2M)+
exp (-,Irlz)+(r3
-2-(t+t_’+t-t+‘).
4r 12
+ tj’)D.
Here p1 and pz are the momenta of the particles and D is the mass
difference of neutron and proton (in energy units). “This Hamiltonian”, says Yukawa, “is equivalent to Heisenberg’s Hamiltonian if we
take for ‘Platzwechselintegra1’ J(r) = -(g2/r)exp ( 4 r ) . . .”, except for
neglect of forces between like particles (n-n orp-p).
The sign that Heisenberg assumed for J(r) led to the deuteron having zero spin, but the true spin is one. Yukawa assumed that he could
correct this by choosing appropriately the sign of his charge exchange
interaction, but he was wrong. To the extent that Heisenberg regarded
the exchange interaction as phenomenological, he could choose its
sign to be either that of the exchange force in atoms (and get the
wrong spin dependence of the forces), or the opposite (and get it
right). However, Yukawa’s theory contains a definite mechanism for
producing the exchange interaction, and it is a fundamental theory
that makes a definite (incorrect) predi~tion.~O
He realized later that
other versions of the meson theory (e.g., other spin choices) would
need to be explored, to fit the observed nuclear forces. Regarding the
size of the “charge” g and the range of the force, given by l / A , he says:
Rough estimation shows that the calculated values agree with the experimental results, if
we take for L the value between 1012cm” and 1013cm” and for g a few times of the
elementary charge e, although no direct relation between g and e was suggested in the
above considerations.g*
The theory presented to this point is classical or semiclassical, from
the viewpoint of field theory; i.e., it is a quantum mechanical description of nucleons interacting through a classical U-field. The description of this field in vacuum parallels Maxwell’s treatment of the electromagnetic potential. However, there is another interpretation for
the wave equation for U: it can be regarded as the relativistic
Schrodinger equation (also called the Klein-Gordon equation) for a
106
Laurie
M. Brown
free particle, so that U is the particle’s wave function. The range
parameter A, is then the inverse Compton wave length of the particle,
rnclh.
This interpretation calls for the second quantization of the U- and
U-fields, and it shows immediately that the quanta have the mass m =
~ , I / c In
. ~the
~ second quantized field theory, U(x, t ) is an operator that
either destroys a positively charged quantum at x or creates a negatively charged quantum; U ( x , t ) does the reverse.
Assuming1 = 5 x 1012cm-1, corresponding to a nuclear force range
of 2 x 10-13cm, Yukawa predicts that the mass of the U-quantum (of
either charge) should be about 200 electron masses. He notes,
As such a quantum with large mass and positive or negative charge has never been found
by the experiment, the above theory seems to be on a wrong line. We can,show, however,
that, in the ordinary nuclear transformation, such a quantum can not be emitted into
outer space.
In a sense, this is obvious, since such an emission would violate the
energy principle; the energy available in nuclear transformation of the
ordinary sort is not larger than about 10 MeV, while a mass equivalent
to 200 electrons requires more than 100 MeV. Yukawa makes a less
obvious argument, though, which shows the relationship between the
mass of the quantum and the range of the force; at the same time, it
relates the concepts force field and particle creation. 93
He does this by solving the wave equation for the U-field by the
Green’s function method, and showing that in cases where the energy
of the neutron-to-proton transition (for example) is less than mc2, the
U-field is exponentially damped, falling off rapidly beyond the distance l/,I. On the other hand, if the transition energy exceeds mc2,
then U is an undamped propagating wave and the U-quantum
emerges from the nucleus, or to use Yukawa’s phrase, “can be emitted
in outer space.”
Yukawa thus explicitly predicts that U-quanta should be observable
when sufficient energy is available, and he concludes:
The reason why such massive quanta, if they ever exist, are not yet discovered may be
ascribed to the fact that the mass m u is so large that condition I W r W p I >m& is not
fulfilled in ordinary nuclear transformation.
Yukawas’s Prediction of the Meson
107
These are the possibilities that arise from the strong interaction of
the U-quantum with the nucleons:
(a) A neutron becomes a proton, emitting a negatively charged
quantum; this quantum is absorbed by a proton in the same nucleus, the proton becoming a neutron.
(b) A proton becomes a neutron, emitting a positively charged
quantum; this quantum is absorbed by a neutrofl in the same
nucleus., the neutron becoming a proton.
(c) The same processes described by (a) and (b), but with the second
interaction occurring in another nucleus. This provides a force
acting between nuclei, responsible for nuclear scattering and
nuclear reactions.
(d) The same production processes as in (a) and (b), with the
U-quantum emitted and moving as a free particle.
In case (d), one can ask for the ultimate fate of the U-quantum.
Evidently, it may have a strong reaction at a nucleus far removed from
its birthplace, or it may undergo some other transformation as a free
particle in free space. (See Figures 1, 2, 3.).
8. The radioactive meson
Yukawa assumes that the U-quantum (or meson) interacts not only
with the “heavy particles”, proton and neutron, but also with the
“light particles”, electron and neutrino (actually antineutrino) and
their antiparticles. As with the nucleons, the light particles interact as
a pair, having one charged and one neutral member.94 A negative
meson can be absorbed by the “vacuum”, and raise a negative energy
neutrino to a positive energy electron state, leaving a hole in the Dirac
“negative energy sea” of neutrinos; this hole is an antineutrino. The
process occurs with a much smaller probability than the interaction of
the meson with nucleons; it can be regarded as the radioactivep decay
of the U-quantum, when the latter is a free particle . (Fig. 3). On the
other hand, if the process takes place in the same nucleus in which the
U-quantum is produced, it is regarded as t h e p decay of the nucleus
(Fig. 2), the process described by Fermi and , “as in the theory of
108
Laurie M . Brown
HEISENBERG
FERMI FIELD
YUKAWA
Figure 1. Models of the strong nuclear charge-exchange force.p, p', protons; n, n', neutrons; e;
electron; Y , neutrino; I/; heavy quantum.
F F->
-U.-
n
HEISENBERG
FEW1
>
YUKAWA
Figure 2. Models of the (weak) B decay interactions. (Notation as in Figure 1.)
n
+ U-
MESON PRODUCTION
- - -;&U-
MESON DECAY
I
Figure 3 . Other processes predicted by Yukawa's theory. (Notation as in Figure 1.)
Yukawas’s Prediction of the Meson
109
internal conversion of y-rays, the intervention of the photon does not
affect the final result. Our theory, therefore, does not differ essentially
from Fermi’s theory.”95
While Fermi specifically disclaimed any analogy between his p-decay theory and Dirac’s hole theory of electromagnetic pair production,
Wick did invoke the analogy in his treatment of positron p decay.
Yukawa, independently of Wick, also demonstrated that the creation
of an electron and an antineutrino, both with positive energy, is equivalent to the creation of an electron together with the destruction of
a negative energy neutrino (i.e., to raising a negative energy neutrino
to a positive energy electron state, leaving behind a hole). Since the
process we have described is essentially analogous to the protonneutron transition (destruction of proton and creation of neutron),
Yukawa adds a new light particle source, 4 n g ‘ q kq k )(summed over
the Dirac index k = l . . .4), to the heavy particle source.96 The new
constant g’, of the same dimensions as g, is assumed to be much
smaller than g.
In Yukawa’s view the beta decay of a nucleus is, accordingly, a
double process : a neutron changes to a proton emitting a virtual
negative meson that subsequently (in a time too short to be
observable, even in principle) decays into an electron and an antineutrino. Positron 8-decay occurs analogously, with a proton turning
into a neutron. Taking into account the short range of the potential
(l/r)exp(Ar), Yukawa demonstrates that the Fermi constant (that
appearing in Fermi’s theory described in Sect. VI) is equal to
4xgg‘/12.Fermi’s constant is related empirically to the rate of/3 decay
(by Fermi’s theory), whileg a n d l are determined by the properties of
the strong interaction. In principle, then, Yukawa’s weak interaction
constant g’ can be determined, and would lead to a prediction of the
radioactive half-life of the meson. Estimates of the half-life were,
however, not made on this basis before 1938.9’
I emphasize that Yukawa introduced two new coupling constants or
“charges”, having the same physical dimensionality as that of electric
charge, but of very different strengths. The larger one measures the
strength of coupling of the meson to the heavy particles; it accounts
for the exchange of mesons that gives rise to the binding of nucleons to
form nuclei, for the scattering of nucleons on each other, and for the
production of free mesons when sufficient energy is available. The
110
Laurie M. Brown
other charge is much weaker (about lo-* times smaller than the strong
coupling constant). It measures the coupling strength of the meson to
the light particles, electron and neutrino, and accounts for the weak
interactions: nuclear beta decay, free neutron beta decay, and meson
decay. While Heisenberg’s and Fermi’s theories each involve only one
coupling constant, Yukawa’s theory is in much better accord with
nature.
In his concluding summary, Yukawa does not refer to a finite
life-time for the free meson, but assumes that mesons may be present
in the cosmic ray beam and may be absorbed by the earth. Should
negative quanta be in excess, the earth could be charged to a negative
electrical potential. Some cosmic ray workers had suggested that the
latter could be responsible for the acceleration of cosmic rays9* These
remarks are not well-founded, but another one is prophetic: “The
massive quanta may also have some bearing on the shower produced
by cosmic rays.” Indeed, the main origin of the electromagnetic cascade or shower in cosmic rays is the neutral pion, which became an
essential requirement of the theory when the nuclear forces were
seen as charge-independent, about two years later.
9. The meaning of the meson
One of Yukawa’s first students wrote recently that the meson theory
opened up a new fundamental view of Nature. This event might be regarded as a miracle
in the history of Japanese physics. Through all of his works and thoughts, we are irnpressed by the simplicity of approach, the unfailing intuition and the creativity of a great
master, which are deep-rooted in Yukawa’s culture?
Here the meson theory-is said to enlarge the- class of elementary
particles, providing a new view of nature; it is called a miracle for
Japanese physics, in which native cultural traits may have played a
significant role. There may be other “meanings” for the meson, but I
shall deal with the subject mainly under these rubrics.
At the beginning of Section 3 we quoted Yukawa on the usage of
the term “elementary particle” at the beginning of the 1930’s; it
meant simply electron or proton, and there was a prohibition of new
elementary objects that was sometimes unspoken, at other times
Yukawas’s Prediction of the Meson
111
explicit.100 When Pauli proposed a new type of particle, the neutrino,
he waited three years to publish his idea - and then did so only in the
form of a discussion remark.lol When Dirac was “led to a new kind of
particle caused by a hole in the distribution of negative-energy states,”
and the symmetry properties of the theory suggested that the particles
have positive charge and electronic mass, Dirac still called it a proton:
I just didn’t dare to postulate a new particle at that stage, because the whole climate of
opinion at that time was against new particles. So I thought that this hole would have to
be a proton. I was very well aware that there was an enormous mass difference between
the proton and the electron, but I thought that in some way the Coulomb force between
the electrons in the sea might lead to the appearance of a different rest mass for the
proton. So I published my paper on this subject as a theory of electrons and protons.102
Reluctance to admit new elementary particles to help explain the
puzzling phenomena of nuclear physics went beyond abhorrence of
the ad hoc, and beyond aesthetic judgement. It seemed narural to
expect the quantum generalization of classical mechanics to fail in that
much smaller region of space, the atomic nucleus. Moreover, the nuclear size is about the same as the “classical electron radius” (about
cm), where H. A. Lorentz had predicted that classical electrodynamics would break down. Physicists were predisposed to look
for an explanation of the crisis of nuclear physics in the breakdown of
dynamics, rather than to postulate new particles or new forces.lo3
Bohr’s insistence upon the failure of energy conservation in the
nucleus is well-known. Heisenberg’s interest in a microscopic universal length persisted even after the muon was discovered in cosmic rays
and Yukawa’s theory of nuclear forces became generally accepted. He
wrote to Pauli in 1938 that he had learned from H. J. Bhabha and W.
Heitler why “explosions” (also called “bursts” or “stars”) should
occur in the cosmic rays, according to Yukawa’s theory, and continues:
It was interesting to me, however, that Bhabha as well as Heitler also obtain [in the
expression for] the force between neutron and proton a term of the formb( J r l- r Z I ) . . .
[i.e., an infinite contact force] This result is very agreeable [sehr symporisch] to me,
because it shows again that one cannot make further progress without the universal
length.IM
These are some of the reasons why Western physicists did not anticipate Yukawa’s nuclear force model. When the “heavy electron” or
112
Laurie M . Brown
“mesoton” (as the muon was then called) was found, Leon Brillouin
identified it as Yukawa’s U-quantum. Referring to Heisenberg’s
suggestion to use the Fermip-decay mechanism as a realization of the
charge-exchange nuclear force, Brillouin said:
A Japanese, Yukawa, found in 1935 a very simple way of improving the theory. “Fermi’s
Field” surrounding a heavy particle corresponds to the exchange of an electron with a
neutrino. Yukawa had the idea of admitting that this field should actually correspond to
the exchange of one new particle differing both from an electron and a n e u t r i n ~ . ’ ~ ~ ~ ’ ~ ~
(original emphasis)
On occasion the scientific process is described by political
analogieslo7; sometimes the analogy is mechanical or thermodynamic.los Such analyses seem inappropriate to apply to
Yukawa’s achievement, for they emphasize a shift, perhaps profound,
in the understanding of a given system. But Yukawa’s prophetically
entitled “On the Interaction of Elementary Particles. I.” is a door
opening on a world of high energy processes, involving the creation
and annihilation of new ephemeral substances (the mesons, unstable
leptons, strange and charmed particles, etc.) of astonishing novelty.
One is justified in regarding this as a lesser revolution than, say,
quantum theory or relativity, only by placing an exaggerated value on
modes of thought, as opposed to understanding the content of nature.
From a certain standpoint, we may regard atomic and nuclear forces
as having paramount scientific interest, but if the physicist’s task is to
discover new phenomena, as well as deeper ways of understanding the
old phenomena, then the prediction of the meson and its relation to
nuclear forces is a towering achievement. Indeed, in most episodes of
the history of physics, a necessary preliminary to the dynamical treatment of a system, is the discovery of its constituents. The importance
of this point has been stressed especially by Talietani.
Although Yukawa has his own, probably unique, philosophical
orientation, it would be as inappropriate to discuss Yukawa’s thought
without reference to the philosophical ideas of Sakata and Taketani as
it would be to discuss Einstein’s thought without reference to Ernst
Mach. To compare the two cases may appear to be absurd; after all,
Sakata and Taketani werestudents of Yukawa, while Mach was almost
forty years older than Einstein and influenced the latter by his writings. Nevertheless, the relationship between Yukawa and his brilliant
Yukawas’s Prediction of the Meson
113
students was a complex and reciprocal one, and was especially important in the social and political circumstances of Japanese physics in the
1930’~.~O~
Sakata spent the year after graduation on a fellowship at the Riken
in Tokyo, under the guidance of Tomonaga who, together with
Nishina, was working on several processes involving the positron.
Sakata helped Tomonaga to calculate the creation of a positron-electron pair by a y ray incident upon a nucleus, but they were beaten to
publication by W. Heitler and F. SauterllO. After Sakata moved to
Osaka, he and Yukawa calculated the probability for creation of an
electron-positron pair by a nuclear transition in which no y ray is
emitted, a process rather similar to internal conversion.lll Then
stimulated by a suggestion of Guido Beck, who visited Japan at this
time, they considered the process in which a nucleus captures an electron from the innermost atomic orbit (K-shell), at the same time
emitting a neutrino.l12
The paper of Yukawa and Sakata on the K-capture process was
important for two reasons. It was the first treatment of this fundamental process, and it uses Yukawa’s meson theory. Between the first
meson paper and Yukawa’s “short note” identifying the cosmic ray
“heavy electron” with his U-quantum, Yukawa published seven papers, all in the Proceedings of the Physico-Mathematical Society of
Japan, five of them jointly with Sakata.
Sakata wrote that Taket‘ani used to visit the Osaka group about
once a month, after his graduation from Kyoto University in 1934.
“He always had ideas about the theory of the nucleus and we used to
discuss it until late at night. Sometimes he talked about Hegel’s logic
and Yukawa would listen with great interest.”l13 Taketani’s graduation thesis at Kyoto had been a study of the logical structure of quantum mechanics, which served as the starting pointsfor his “three-stage
methodology” of physics. This adds a third “substantialistic” stage
between the “phenomonological” and “fundamental” stages that are
often viewed as part of the development of a particular theory.
(Taketani uses the term “essentialistic” for the third stage.) In the
substantialistic stage one recognizes the substances in the model; for
example, electrons and the nucleus are identified as the constituents of
the Bohr-Rutherford atom. Taketani’s methodology is materialist,
emphasizing concrete objects, and it is dialectical, since the final stage
8 Centavrur xxv
114
Laurie M . Brown
of one theoretical development can become the beginning stage of the
next. 114
Although Sakata was the more orthodox Marxist, Taketani was
more active politically and wrote for a radical journal called World
Culture (Sekai bunka) that served as an intellectual spearhead of the
movement against fascism. In 1938 there was a crackdown, and
Taketani left Kyoto to “seek refuge” with a friend in Kobe. Then:
Three days after I had once again changed my Kobe lodging, some plainclothesmen
forced themselves into my apartment while I was asleep and arrested m e . . . After a
month I was taken to the Kawabata police station, which was responsible for investigations related to Kyoto University. . . The unlawful acts for which I was held were: my
analyses of quantum mechanics, my analyses of the development of nuclear physics, and
my methodological approach to the meson theory - in short, my research activities on
natural dialectics. I was forced to state that I had participated, through my research, in
the cultural movement of the popular front under instructions of the Comintern, thus
helping to promote the Communist Party in Japan.”’
Sakata and Taketani do not claim to have influenced Yukawa’s meson
prediction, except most indirectly. Sakata wrote, “Yukawa is really
not a dialectical materialist.”l16 Tetsuo Tsuji recently interviewed
Taketani, and asked about his contacts with Yukawa in Osaka, with
the reply:
H e is such a genius-type, you know; he listened to me, saying only “yes, yes,
Detailed discussions on my’ methodology were mainly with Sakata.11’
. . .”
Yukawa’s attitude shows up in his preface to a recent intellectual
biography. Asked by his poet-biographer if a dog-motif appearing in
Yukawa’s published poems represents “fear”, and whether Yukawa
was fearful or confident in proposing the meson, his reply was that he
had perfect confidence. 118 PoincarC argued that physics should be
based upon hypothesis, but like Descartes, Yukawa viewed his theory
as self-evident truth. He felt that this kind of revelation is a most
valuable approach to fundamental physics. After the discovery of the
cosmic ray meson, however, he began to have doubts and worried
about its reluctance to conform to his predictions - but his confidence
was then restored by the two-meson hypothesis.llg
In the same preface he says that he regarded the divergence problems of quantum field theory as more fundamental than the theory of
Yukawas’s Prediction of the Meson
115
the nuclear force. Using the language of Taketani, he asserts that his
main intellectual interest lies in the “essentialisticY7
stage of the theory,
while the meson theory was a contribution to the “substantialistic”
stage. He took these up again in 1942, and this led eventually to an
interest in non-local field theory, which he introduced in 1950 to try to
deal with the problem of divergences (infinities) and newly discovered
particles.
While expressing his appreciation of Taketani’s methodology, he
says that in the future there must be a fusing together of the last two
stages, the substantialistic and the essentialistic. Quoting the Chinese
poet Li Po (“The universe is an inn that accomodates all things; time is
a traveler of one hundred generations.”), he says that one day in 1966,
he conceived of the idea of the “elementary domain”, a modification
of the ideas of space-time and causality - requiring the use of difference equations, rather than differential equations.120
Although Yukawa does not identify himself with the Sakata-Taketani methodology or with their political philosophy, his close association with them in the 1930’s helped to relieve his sense of scientific
isolation, while strengthening his independence of the various “authorities” - among them the state and its institutions, the family and
its traditions, and intellectual authorities, both at home and abroad.
10. Acceptance of the mesop theory
The story of the discovery of the “heavy electron”, the particle now
known as the muon, in the cosmic rays does not belong to the “preNeither process is
diction” theme, but rather to that of
ever simple, and the sorting out of “soft” and “hard” components of
the cosmic rays, the observation of cloud chamber tracks that had too
little radiation interaction to be electrons (yet could not be protons, as
they were almost as often negative as positive), and the other
observations and shifts of sentiment that eventually convinced the
experimentalists that they were viewing new particles of intermediate
mass will be taken up in another place. What is important here is that
by July 1937, the experimental announcements had been made, and
very soon afterwards Yukawa wrote a “short note” to point out that
his theory had predicted just such particles.122
One of the first European theorists to apply and generalize
116
Laurie M . Brown
Yukawa’s theory was Nicholas Kemmer, who summarizes the situation in the passage that follows. After remarking that the origin of
nuclear forces in the first half of the 1930’s was “definitely
overshadowed as a topic for theoretical speculation by the everpresent
problem of 137, of the strength of electromagnetic interaction^,^^ he
continues:
This then was the mood which made it possible for Hideki Yukawa’s paper to appear in
the Proceedings of the Physico-Marhematical Sociery of Japan in 1935 and to remain
virtually unnoticed and certainly entirely unappreciated. Though Yukawa’s idea was
basically so simple and also so clearly stated, it attracted no attention. Perhaps part of the
explanation was that the journal in which it was published was not widely read. But this
cannot be the whole story for in those days the volume of work published in this field was
so small compared with today that any serious minded student would find no difficulty
whatever in taking note of the contents of all relevant papers in wharever journal they
were published. More important perhaps was the fact that among the leaders of theoretical physics in Western Europe all important results were instantly communicated at
private meetings or by correspondence, while Yukawa’s ideas never even started being
spread by this “grapevine” method. But having said all this, it is quite clear that Hideki
Yukawa in 1935 was ahead of his time and found the key to the problem of nuclear forces
when no other theoretical physicist in the world was ready to accept it.
All this was changed in 1937 after Anderson announced his discovery in cosmic radiation of a particle of approximately the mass required by Yukawa’s theory. Within weeks
we were studying and attempting to extend Yukawa’s ideas. And within a few months, if
not weeks, workers in Japan and in Europe discovered that they were thinking on
practically identical lines and Yukawa’s ideas had been completely assimilated. What can
only be called a joint enterprise from that moment onwards was of course abruptly
terminated by the outbreak of war.lZ3
The “joint enterprise” to which Kemmer refers, and in which Kemmer
himself played a leading role, consisted of applying the meson theory
to new problems (e.g., the magnetic moments of the neutron and
proton) and in generalizing it (e.g., with inclusion of a neutral meson).
There was also the effort to match the properti’es of the cosmic ray
“heavy electron” to those expected for the nuclear force meson. Since
the muon has no strong interaction, this could not really be done, but
various types of quantum field, various spins and “mixtures” were
tried.
One of the last international conferences that was held before
World War 11, took place in Warsaw, May 30 to June 3, 1938. Entitled “New Theories in Physics”, it was organized by the International Institute of Intellectual Co-operation, in collaboration with the
Yukawas’s Prediction of the Meson
117
International Union of Physics and the Polish Intellectual Co-operation Committee. Participants ranged from Niels Bohr to Eugene P.
Wigner, by way of de Broglie, Eddington, von Neumann, etc. Of eight
speakers, three (L. Brillouin, 0. Klein, H. A. Kramers) dealt with
Yukawa’s meson theory, citing him by name twelve times.124A year
earlier no one who had not visited Japan would have known his name.
11. Summary and Conclusion
At the time when Hideki Yukawa graduated from Kyoto University in
1929 as a highly motivated and partly self-taught theoretical physicist
and began his research on nuclear theory, the empirical knowledge of
nuclear physics accumulated since the start of the century had led to a
crisis. It was believed that electrons and protons must be the constituents of the nucleus, for they could be observed, in special circumstances, leaving the nucleus, and because they were the only
known elementary material particles.
The solution to the nuclear problem was therefore thought to lie in
a new dynamics, or possibly in a modified microscopic structure of
space and time. This turned out not to be the case; instead, the major
paradoxes were resolved by the experimental discovery of new
elementary particles, the neutron and the positron, and by Pauli’s
theoretical invention of the hard-to-observe neutrino. Using these
new particles, Heisenberg and Fermi made theories which provided,
with some later modification, the phenomenological basis for our
present understanding of the strong and the weak nuclear interactions.
There remained the problem of providing a fundamental theoretical
foundation for these phenomenological theories (or, at least, a
deeper-lying level of phenomenology), and this was given by the meson theory of Yukawa. I have studied in detail its conceptual development through the first meson article.
Ackno wledgernents
I wish to acknowledge initial assistance in support of this work by the
Research Committee of Northwestern University. I want especially to
thank Donald F. Moyer, Yoichiro Nambu, Ralph E. Segel and Martin
J. Klein for valuable discussions and moral support.
118
Laurie M . Brown
Appendix I. Historiographic notes
1. General works in English.
(a) Related to Japanese physics:
Shigeru Nakayama, David L. Swain, E n Yagi, Science and
Society in Modern Japan, Selected Historical Sources (MIT
Press, 1974). [This contains “An Annotated Bibliography
of English Language Works on the Social History of Modern Japanese Science”, by James Bartholomew. The section headed The Prewar Period (1920’s to early 1940’s)
says: “Virtually nothing on this period has been available
prior to the publication of this book”, Science and Society in
Modern Japan. ]
Kenkichiro Koizumi, ‘The Emergence of Japan’s First Physicists: 1868-1900”, Historical Studies in the Physical Sciences 6 (ed. by Russell McCormmach), 1975, pp. 3-108.
Various articles in Japanese Studies in the History of Science
(Nippon Kagakusi Gakkai), published by the History of
Science Society of Japan.
(b) Early reviews on the meson and on nuclear forces:
N. Feather, “Atomic Physics”, Reports on Progress in Physics
2, (1935), 74-96; N. Feather, ibid. 3 (1936), 66-88.
H. A. Bethe and R,.F. Bacher, “Nuclear Physics” (Parts A, B,
C), Reviews of Modern Physics 8 (1936), 82-229; H. A.
Bethe, ibid. 9 (1937), 71-244; M. Stanley Livingston and
H. A. Bethe, ibid. 9 (1937), 246-390.
W. Heitler, “Cosmic Rays”, Reports on Progress in Physics 5
(1938), 361-389.
R. Peierls, “The Meson”, ibid. 6 (1939), 78-94.
H. J. Bhabha, “The Theory of the Elimentary Particles”,
ibid. 10 (1944-45), 253-271.
Wolfgang Pauli, Meson Theory of Nuclear Forces (Interscience, 1946 and 1948).
Gregor Wentzel, Quantum Theory of Fields (Interscience,
1949).
Viivapriya Mukherji, “A History of the Meson Theory of
Nuclear Forces from 1935 to 1952”,Archivefor History of
Exact Sciences 13 (1974), 27-102.
Yukawas’s Prediction of the Meson
119
(c) Useful collections:
H. Yukawa, Scientific Works, edited by Yasutaka Tanikawa
(Iwanami Publishers, Tokyo 1979). H. Yukawa, Creativity
and Intuition; A Physicist Looks at East and West
(Kodansha, 1973), translated by John Bester.
Shoichi Sakata, Scientific Works (Publication Committee of
Scientific Papers of Prof. Shoichi Sakata, 1978). This includes philosophical papers, translated into English by his
students.
Sin-itiro Tomonaga, Scientific Papers, edited by Tatsuoki
Miyazima. (Misuzu Shobo, vol. I, 1971, in English; vol. 11,
€976, mostly in Japanese.)
Supplement of Progress of Theoretical Physics, especially:
Nos. 1 and 2, 1955, “Collected Papers on Meson Theory”;
No. 3, 1956, “Collected Papers on Nuclear Forces”; No.
50, 1971, “Philosophical and Methodological Problems in
Physics.”
2. Unpublished works in English.
Satio Hayakawa, “Development of Cosmic Ray Research in
Japan,” Papers of the 1966 Summer Physics Colloquium of
the Peking Symposium (Peking, July 1966). S. Hayakawa,
“Hideki Yukawa - Nobel Prize for Physics in 1949” (written in 1969, unpublished).
Letters in the Archive for History of Quantum Physics:
Nagaoka to Goudsmit (1930); Nishina to Goudsmit
(1926-30); Nishina - Bohr correspondence (1923-40).
Letters in the Nagaoka Collection, National Science Museum,
Ueno Park, Tokyo.
Letters between Nishina and Dirac, Nishina Memorial
Foundation, Bunkyo-ku, Tokyo.
Workshops and interviews, 1978-79, conducted in Japan by
United States - Japan Collaboration (USJC 1-10). See
Appendix I11 for names of collaborators.
3. Books and articles, previously available only in Japanese and
translated for this project.
Hideki Yukawa (assisted by Hisao Sawano), Tabi-bit0 (the
traveler), (Asahi Press, Tokyo, 1959); translation by Rikutaro Yoshida, about 200 pages.
120
Laurie M . Brown
Yoichiro Nambu, “Soryushiron” (particle research) in Butsuri
(Bull. Jap. Phys. SOC.)32, vol. 10 (1977), 773-778; trans.
by R. Yoshida.
Shoichi Sakata, “Reminiscences of Research on Meson
Theory,” in H. Yukawa, S . Sakata, M. Taketani, Quest f o r
Elementary Particles (Keiso Shobo, 1965); originally published in At the Battlefield of Truth (Mainichi Shin Bunsha,
1951); translation by Noriko Eguchi, 43 pages, second
translation by R. Kawabe, Also “Passages on the history of
the two-meson theory,” trans. by Masayuchi Nagasaki.
Sin-itiro Tomonaga, “Reminiscences of My Research - from
old records,” in Butsuri (Bull. Jap. Phys. SOC.)32, voi. 10
(1977), 767-773; translation by Noriko Eguchi.
H. Yukawa, “Ancient History of Beta Decay,” in Shizen
(Nature), July, 1975, pp. 28-39; Special Issue on Forty
Years of Meson Theory; translation by R. Yoshida.
Yasutaka Tanikawa, “Genesis of Meson Theory,” Shizen,
July, 1975, pp. 40-51; translation by R. Yoshida.
Masa Takeuchi, “Remembrance of Studies of Mesons in the
Cosmic Rays,” in Shizen, July, 1975, pp. 52-59; translation
by R. Yoshida.
Sin-itiro Tomonaga, “German Diary - 1938,” from M y
Teachers and My Friends (Kodansha, 1976); translated by
Fumiko Tanihara, 9 pages.
H. Yukawa, S . Sakata, M. Taketani, A Dialogue on Modern
Studies (Keiso Books, Tokyo); selections translated by R.
Yoshida, about 30 pages.
Mituo Taketani, “The Meson Theory and the Methodology of
Three Stages,” in History of Japanese Physics, vol. I. (The
Physical Society of Japan Edition, To’kai University Press,
1978); translated by Yoichi Fujimoto, assisted by
Masayuchi Nagasaki.
Shoichi Sakata, “The Background to the Development of
Yukawa’s Meson Theory,’’ Shizen, August, 1946; reprinted
in S. Sakata, Collected Essays, vol. I, Physics and Method,
(Iwanami, 1972) p. 97-107; translation by R. Kawabe.
S. Tomonaga, H. Yukawa, S . Taketani, Y. Fujimoto, “Thirty
Years of Particle Physics (a symposium)” in S. Sakata, The
Yukawas’s Prediction of the Meson
121
Creation of Science and Peace (Iwanami, 1961), translation
by R. Yoshida. Also, in the same book, “Letters to and
from C. F. Powell,” translation by R. Yoshida.
S. Tomonaga, “A Sketch of Developments in Physics in the
Last Quarter Century,” Butsuri (Bull. Jap. Phys. SOC.) 6,
vol. 5 (1950), 340-350, translation by R. Yoshida.
M. Konuma, “Birth of the Theory of Two Neutrinos,”
Soryushiron kenkyu 38 (1968), 482-4, translation by M.
Konuma.
Appendix 11
Introduction to W. Heisenberg, Uber den Bau der Atomkerne,’ by
Hideki Yukawa. [From Journal of the Physico-Mathematical Society
of Japan 7, (1933), 195-205; translated from the Japanese by Rikutaro Yoshida; the footnotes are Yukawa’s].
Since Chadwick suggested the neutron as the theoretical explanation of the experiments of Curie, Joliot, etc., attempts to explain the
systematics of atoms assuming that the nucleus consists of protons and
neutrons began to possess considerable meaning. If, under the assumption that protons and neutrons make up shells obeying Pauli’s
exclusion principle, protons and neutrons are added one by one successively, we are able to list the nuclei from H 1 to Aj6 (although H3
and He5 are not known experimentally); not only that, but the chief
difficulty of the hypothesis that nuclei consist of protons and electrons,
namely the fact that the nucleus of NI4 obeys Bose statistics, is
explained by the hypothesis that NI4 consists of 7 neutrons and 7
protons, both obeying Fermi statistics. However, it is difficult to
explain the nuclei heavier than ClJ7as consisting only of protons and
neutrons (of course, there is no problem in admitting a particles as
secondary elements), and perhaps the presence of electrons within the
nucleus must be admitted.2 This point has not been resolved either
1. Zeit. f. Phys. 77 (1932); 78 (1932), 156; after the present work,a third paper [Zeit.f. Phys.
80 (1933), 5871 was published.
2. E.g., J . H. Bartlett, Jr.;Phys. Rev. 42 (1932), 145.
122
Laurie M . Brown
way, but basically the behavior of electrons in nuclei is difficult to
understand with present day quantum mechanics, and the fact that p
rays come out of certain radioactive atoms with continuous energy
values that do not seem to be due to influences received outside the
atom, and that the decay constant does not vary with the speed of the
p ray, make one doubt the validity of the law of energy conservation
and to further imagine that the electrons lose their individuality inside
the n u ~ l e u s . ~
In this paper Heisenberg ignored the difficult problems of electrons
within the nucleus, and under the assumption that all nuclei consist of
protons and neutrons only, considered what conclusions can be drawn
from the present quantum mechanics. This essentially means that he
transferred the problem of the electrons in the nucleus to the problem
of the make-up of the neutron itself, but it is also true that the limit to
which the present quantum mechanics can be applied to the atomic
nucleus is widened by this approach. Though Heisenberg does not
present a definite view on whether neutrons should be seen as separate entities or as combinations of a proton and an electron, this
problem, like the @ decay problem stated above, cannot be resolved
with today’s theory. And unless these problems are resolved, one
cannot say whether the view that electrons have no independent existence in the nucleus is correct.
REFERENCES
1. Hideki, Yukawa, “On the Interaction of Elementary Particles. I.”, Proc. Phys.-Math. Soc.
Jupun I7 (1935), 48-57, (Also read Nov. 17, 1934, at a regular monthly meeting of the
Society at the Tokyo Imperial University.)
2. Yukawa called his particles “heavy quanta” or “U-quanta”. The name meson refers to the
particle’s mass, intermediate between that of the electron and the nucleon. (The last term is
the generic name for the nuclear particles, proton and neutron, nearly equal mass.)
Before about 1948, when it became known as the pi-meson or pion, it was referred to by
other names as well, such as heavy electron, burytron, mesotron, etc. The designation meson
is perhaps due to H. J. Bhabha (Nature 143 (1939), 276). For a discussion of this point, see
V. Mukherji, “A History of the Meson Theory of Nuclear Forces from 1935 to 1952”,
Archive for History of Exact Sciences 13 (1974), 27-102, p. 38.
3. N. Bohr, Furaday Lecfure, Journ. Chem. SOC. (1932), 349; N. Bohr, “Atomic stability and
conservation laws,” Convegno di Fisica Nucleare, Rome 1932.
Yukawus’s Prediction of the Meson
123
3. W. Heisenberg, “Uber den Bau der Atomkerne”, Zeir. f. Phystk 77 (1932), 1-11; 78
(1932), 156-164; 80 (1933), 587-596. (Part I and part of Part I11 are given in English
translation in D. M. Brink, Nuclear Forces (Oxford, 1965), 144-160). Heisenberg’s theory
was the first systematic attempt to build a nuclear model out of neutrons and protons.
4. E. Fermi, “Tentativo di una teoria dell’emissione dei raggi ‘beta”’, La Ricerca Scientifica
4(2) (1933), 4 9 1 4 9 5 ; “Tentativo di una teoria dei raggi j3”, Nuovo Cimento 2 (1934),
1-19; “Versuch einer Theorie derp-Strahlen. I.”, Zeirf. Phys. 88, (1934) 161-171. (The
last paper is given in English translation in Charles Strachan, The Theory of Beta Decay
(Pergamon Press, 1969), 107-128.)
5. Fermi’s papers on beta decay did not discuss the strong forces responsible for nuclear
binding, but as discussed below, there were a number of attempts by others to make a
unified theory of strong and weak forces based solely on Fermi’s beta-decay interaction or
some modification thereof.
6. P. Jordan and 0. Klein, Zeit. f. Phys. 45 (1927), 751-765. (See Sect. 5 below for the
meaning of this term.)
7. H. Yukawa and S. Sakata, “On the Interaction of Elementary Particles. II.”, Proc. Phys. Math. SOC.Japan 1 9 (1937), 1084-93; H. Yukawa, S. Sakata, and M. Taketani, Part 111,
ibid. 20 (1938), 319-40; H. Yukawa, S. Sakata, M. Kobayasi, and M. Taketani, Part IV,
ibid. 20 (1938), 7 2 0 4 5 .
8. The earliest reference to Yukawa appears to be J. R. Oppenheimer and R. Serber, Phys.
Rev. 51 (1937), 1113 (sent June 1, 1937). For a discussion of the “unfavourable remarks”
of Oppknheimer and Serber and the coolness of reception of the theory, see Mukherji, loc.
cit., pp. 35-37 and 96-97.
9. E. C. G. Stueckelberg, Phys. Rev. 52 (1937), 41-42 (sent June 6, 1937).
10. Seth H. Neddermeyer and Carl D. Anderson, Phys. Rev. 51 (1937), 884-886; J. C. Street
and E. C. Stevenson, Phys. Rev. 51 (1937), 1005; Y. Nishina, M. Takeuchi, and T. Ichimiya,
Phys. Rev. 52 (1937), 1198-1199.
11. Yukawa, “On a Possible Interpretation of the Penetrating Component of the Cosmic Ray”,
Proc. Phys. - Math. SOC.Japan I 9 (1937), 712-713.
12. See, e.g., L. Jfmossy, Cosmic Rays (Clarendon Press, Oxford, 1948). Throughout this
monograph the “cosmic ray meson”, i.e., the muon, is identified as Yukawa’s particle and
only distinguished from it in an appendix.
13. Cf. Yukawa, 1949, in Nobel Lecrures, Physics 1942-1962 (Elsevier Pub. Co., Amsterdam,
1964), p. 130.
14. J. R. Oppenheimer, “Thirty Years of Mesons”, Physics Today, Nov. 1966, 51-58.
15. H. A. Bethe, “Mesons and Nuclear Forces”, Physics Today, $eb. 1954, 5-11.
16. H. A. Bethe in Exploring the History of Nuclear Physics (American Institute of Physics,
New York, 1972), ed. Charles Weiner, assisted by Elspeth Hart, p. 123.
17. The family name Yukawa was assumed by Hideki in 1932 when he married Sumi Yukawa
and was adopted by her father Genyo, an Osaka physician. The practice of adopting the
younger son of one family into a family without a son is quite common in Japan; Hideki
Yukawa’s father Takuji had also been adopted in this way.
18. H. Yukawa, Tabi-bito, unpublished translation by Rikutaro Yoshida. The period described
by this book is from childhood to 1935, the year of publication of Yukawa’s first article on
the meson. Other autobiographical material by Yukawa in Japanese: Butsurigaku ni
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Laurie M. Brown
kokorozashite (Aspiring for Physics; Kyoto, 1944); Meni mienai mono (Of things that cannot
be seen; Kobunsha, 1942); Shinri no ba ni tachite (In the course of our study), with S . Sakata
and M. Taketani (Mainichi Shimbun, Tokyo, 1951).
19. Yukawa’s youngest brother Masuki Ogawa died in the Second World War; the other three
became university professors. For further details of Yukawa’s family see Yasutaka
Tanikawa, “Introduction and Biographical Sketch” in H. Yukawa, Scientific Works, edited
by Y. Tanikawa (Iwanami, Tokyo, 1979). I am indebted to Professor Tanikawa for a copy in
advance of publication.
20. From a chapter of Yukawa’s book Meni mienai mono (ref. 18), translated by Chihiro
Kikuchi and published as “The Birth of the Meson Theory”, Am. lourn. of Physics I8
(1950), 154-156.
21. After the Meiji Restoration, the samurai Komakitsu Ogawa studied European culture and
read the English language Times “every day until his death”, according to Tabr-bito (ref.
18).
22. For example, in Creativity and Intuition, a collection of Yukawa’s essays in English, translation by John Bester (Kodansha International, Tokyo, 1973). See especially the 1968 essay,
“On learning and life”.
23. See James Bartholomew, “Japanese Culture and the Problem of Modern Science”, in
Science and Values, edited by Arnold Thackray and Everett Mendelsohn (Humanities Press,
1974).
24. Kenkichiro Koizumi, “The Emergence of Japan’s First Physicists: 1868-1900”, Historical
Studies in the Physical Sciences 6 (1975), 3-108, on pp. 82-94. Lawrence Badash,
“Nagaoka to Rutherford, 22 February 1911”, Physics Today, April 1967, 55-60. Rutherford’s reply is given by Eri Yagi, Japanese Studies in the History of Science 3 (1964),
Appendix I, p. 46.
25. Hantaro Nagaoka, The Age of Nuclear Power, as quoted in Tosaka Kimura, Kiyonobu
Itakura, and En Yagi, Nagaoka Hantaro den (Asahi Shinbun, Tokyo, 1973), pp. 39-40.
26. Koizumi, ref. 24, p. 50 ff.
27. The Chinese character for “Elementary”, drawn by Yukawa, was chosen as the logo for the
19th International Conference on High Energy Physics, held in Tokyo in August 1978. It
appears on the cover of the September, 1978 issue of the CERN Courier.
28. Natsume Soseki, Sanshiro, English translation by Jay Rubin (University of Tokyo Press,
1977).
29. This quotation is from a 1948 essay “The Oriental Approach” in Creativity and Intuition
(ref. 22). There are separate essays also on the Taoist writers in this book. See also H.
Yukawa, “Modern Trend of Western Civilization and Cultural Peculiarities in Japan”, in
The Japanese Mind, ed. Charles A. Moore (East-West Center Press, Honolulu, 1967).
30. I refer here to Shoichi Sakata and Mituo Taketani. See e.g., S. Sakata, “My Classics Engels’ ‘Dialektik der Natur’,” Suppl. Prog. Theor. Phys..No. 50 (1971), 1-8; M. Taketani,
“Methodological Approaches in the Development of the Meson Theory of Yukawa in
Japan”, in Science and Society in Modern Japan, ed. S . Nakayama, D. L. Swain, and E. Yagi
(1974, MIT Press, Cambridge, Mass). Taketani’s article is adapted from Supplement of the
Progress of Theoretical Physics No. 50 (1971), 18-24, the latter being the English translation of a part of Taketani’s article in the book Shinri no ba ni rachite (ref. 18). No. 50 of ;he
Supplement has 250 pages under the title: Philosophical and Methodological Problems in
Physics; it consists almost entirely of articles by Taketani and Sakata
Yukawas’s Prediction of the Meson
125
31. Ishiwara was an important theoretical physicist who studied with Einstein and Sornmerfeld
in Germany and returned to Japan in 1915. He worked on both relativity and quantum
theory and is credited with generalizing Bohr’s quantum condition. Afier losing his position
at Tohoku University because of a love affair, he began to write popular scientific books.
Two of these that were read by Yukawa were: Theory of Relativity and Fundamental Problems in Physics.
32. According to Minoru Kobayasi (private communication) Araki lectured in 1926 or 1927.
The connection was with the Hamilton-Jacobi formalism used in celestial mechanics, as
applied to atomic physics. “His lectures were very beautiful, like a classical theatre performance.”
33. Reference 20.
34. Carl F. von Weizsacker recalls being told by Heisenberg that the problem of relativity an!
quantum theory and the electron had been solved by a young Englishman by the name of
Dirac, who was so clever that it did not pay to compete with him. (AHQP interview of
1963).
35. Yukawa, Shizen (Nature), July, 1975, pp. 28-39, Special Issue on Forty Years of Meson
Theory. Unpublished translation by R. Yoshida.
36. Hans A. Bethe, “The Happy Thirties”, in Nuclear Physics in Retrospect; Proceeding of a
Symposium on the 1930’s, 9-31, edited by Roger H. Stuewer (University of Minnesota
Press, 1979). See also: Edward M. Purcell, “Nuclear Physics without the Neutron: Clues
and Contradictions”, Xth International Congress of the History of Science, Proceedings
(Ithaca, 1962), I , 121-133.
37. W. Heisenberg and W. Pauli, Zeif.f. Phys. 47 (1929), 1-61, Earlier treatments involved the
quantization of only the radiation part of the electromagnetic field, while the static Coulomb
potential, for example, was treated classically.
38. Cf. Joan Bromberg “The Impact of the Neutron: B o b and Heisenberg”, Historical Studies
in rhe Physical Sciences 3, (1971), 307-341.
39. Enrico Fermi, Mem. Acad. &Itaka I (Fk) (1930), 139-148 and Zeitf. Phys. 60, (1930),
320-333; a preliminary version is E. Fermi, Nature I 2 5 (1930), 16. According to Emilio
Segrk, Fermi’s motivation for the work on hyperfine structure was similar to that of Yukawa,
i.e., as a bridge between the intra- and extra-nuclear atomic regions. See E. Fermi, Collected
Papers, vol. I., ed. E. Segrk (University of Chicago Press, 1962), p. 328. Afier Fermi’s
paper, the subject acquired a certain vogue: both Pauli and Samuel Goudsmit reported on it
at a meeting of the American Physical Society in Pasadena, California, in June, 1931.
Goudsmit says in a private letter to the author (Feb. 10, 1978): “At that time I always talked
everywhere about hypertine structure.”
40. The Japanese name is Rikagaku Kenkyiisho, or Riken for short. The overriding importance
of this private research foundation to Japanese physics between the two great wars of this
century is emphasized in several articles in Science and Society in Modern Japan (ref. 30).
41. S. Sakata, “Reminiscences of Research on Meson Theory” in H. Yukawa, S . Sakata, M.
Taketani, Quest for Elementary Particles (Keiso Shobo, 1965); originally published in In the
Course of Our Study (1951); see ref. 18. Unpublished translations by Noriko Eguchi and by
R. Kawabe.
42. See, e.g., Charles Weiner, “1932 - Moving into the new physics”, Physics Today, May
1972, 40-49; Ch. Weiner, “Institutional Settings for Scientific Change: Episodes from the
126
Laurie M . Brown
History of Nuclear Physics”, Science and Values, ed. by Arnold Thackray and Everett
Mendelsohn (Humanities Press, 1974), 187-212.
43. Gamow, pp. 55 and 56; emphasis supplied by Gamow.
44. L. M. Brown, “The idea of the neutrino”, Physics Today, Sept. 1978, 23-28.
45. Convegno di Fisica Nucleare, Reale Accademia d’Italia, Atti (Rome, 1932). Apparently
Yukawa did not see Samuel A. Goudsmit’s report on hyperfine structure, where he referred
to Pauli’s suggestion of a neutrino.
46. E. N. da C. Andrade, Reports on Progress in Physics I (1934), 269-320. However, George
Gamow’s Structure of Atomic Nuclei and Nuclear Transformations (Oxford, 1937) argues
that since “the classical electron radius is the same as the distance between nuclear particles”, a yet unknown theory is needed to describe electron behavior within nuclei. See also
Rudolf Peierls, “The Development of Our Ideas on the Nuclear Forces”, Nuclear Physics in
Retrospect, etc. (ref. 36), 183-21 1.
47. D. Iwanenko, Comptes rendus 195 (Aug., 1932), 439-441. Iwanenko wrote: “les electrons
intranucleaires sont reellement trks analogues aux photons absorbts, I’expulsion d’un tlectron ,B etant pareille 3, la naissance d’une particule nouvelle qui, en Ctat d’absorption, ne
possedait pas d’individualitC.”
48. See Bromberg, ref. 38, p. 333. Cf. Brink, ref. 3, pp. 14-16; note that Brink omits those parts
of Heisenberg’s papers which most strongly point up their contradictory assumptions.
49. See ref. 3, Part I, p. 1 1 . (translation from Brink, Ioc. cit.). L. Meitner and H. H. Hupfeld
found apparent deviations from the scattering formula of Klein and Nishina for heavy
elements at large quantum energies. (Naturwiss. 18 (1930), 534-535).
50. Ref. 3, Part 111, p. 595.
51. Ref. 3, Part I, Abstract, “ohne Mitwirkung von Electronen”, which Brink translates “and do
not contain electrons.” In reality, Heisenberg’s neutrons do contain electrons.
52. See G. Rasche, “Zur Geschichte des Begriffes ‘Isospin”’, Arch. His.Exact Sci. 7 (1971),
257-276.
53. Ettore Majorana, Zeit. f. Phys..82 (1933), 137-145.
54. Because of Heisenberg’s picture of the neutron as a proton-electron compound, the mass of
the free neutron was required to be less than the mass of proton plus electron; i.e., the free
neutron was stable. This did not contradict what was known of the neutron at that time. The
“mass defect” of the neutron (whatever its sign) is, in any case, small and did not play a
decisive role in nuclear systematics.
55. By the time of the 1933 Solvay Conference, Heisenberg agreed with Majorana that the sign
of the exchange term should be the opposite of that which he had assumed. Rapporfs du
septiime conseil de physique Solvay, 1933 (Paris, 1934), p. 303.
56. Heisenberg, Part 11, p. 164, The “mass defect” is, in fact, negative, since the neutron is
heavier than the proton.
57. E. Wigner, Phys. Rev. 43 (1933), 252-257. Wigner says that he expects his work to be
applicable, whichever of the nuclear structure hypotheses are adopted. H e mentions the
ideas of several physicists, including Heisenberg, whose model he understands to employ
elementary protons and electrons. but not neutrons.
58. In Enrico Fermi, Collecred Papers, Vol. I (Univ. of Chicago Press, 1962), E. Segrk, Ed. in
Chief, the articles of ref. 4 are reprinted as items 76, 80a, and Sob, with an introduction by
F. Rasetti, one of Fermi’s earliest coworkers. The two articles published in 1934, one Italian
Yukawas’s Prediction of the Meson
127
and the other German, appear to be exact translations of each other, while the 1933 article
is referred to as a “preliminary note”.
59. That the neutron was definitely heavier than a hydrogen atom (a proton plus an electron)
was first shown by an experiment on the disintegration of the deuteron byy rays: J. Chadwick and M. Goldhaber, Nature 134 (1934), 237-238; Proc. Roy. SOC. (London) A151
(1933, 479-493. This same experiment, the first photonuclear disintegration, also showed
that the deuteron was “made of’ a proton and a neutron. Recalling this experiment, Goldhaber said, “I remember being quite shocked when it dawned on me that the neutron, an
elementary particle, as I had by the time already learned to speak of it, might decay by@
emission with a half-life that I could roughly estimate. . . to be about half’an hour or
shorter. . .” “The Nuclear Photoelectric Effect, etc.” in Proceeding of a Symposium, etc.,
pp. 83-110 (ref. 36).
60. According to this, a neutrino and an electron must be present “at the proton” for the reverse
of beta decay to occur. This process is evidently very rare. Fermi does not consider explicitly
the possibility of positron beta decay, which was reported by the Joliot-Curies early in 1934,
but presumably afier Fermi had submitted his beta decay paper. Fermi’s theory, however,
already implied a description of this process (as well as others, such as neutrino capture with
positron emission, capture of an electron from an atomic K-shell, etc.); the application to
the new type of radioactivity of the Joliot-Curies was made by G. C. Wick, Rend. Accademia
dei Lincei (6) I9 (1934), 319-324.
61. Fermi calls this the Dirac-Jordon-Klein method, and refers to P. Jordan and 0. Klein, Zeit.
f Phys. 45 (1927), 751-765 and to W. Heisenberg,Ann. der Physik I0 (1931), 888-904.
62. G. Beck and K. Sitte, Zeit. f Phys. 86 (1933), 105-119; ibid. 89 (1934), 259-260. Their
theory assumed that the B-decay process begins with the virtual production of an electron-positron pair; one particle is then absorbed, while the other is emitted. This theory was
for a time a strong competitor to Fermi’s. Recently Guido Beck wrote to me from Rio de
Janeiro, agreeing that Femi’s paper of 19% brought about “one considerable improvement
to our model, because it attributed to the lost particle, the neutrino, the rest mass zero.. .
But, basically there is hardly a fundamental difference between sayingthat a particle (neutrino) exists but cannot be detected by experiments, or to say this particle is lost.” I am
indebted to Professor V.L. Telegdi for the suggestion that Fermi might have disclaimed the
use of the Dirac hole theory to emphasize his differences with Beck and Sitte.
63. See G. C. Wick, ref. 60. In ref. 1 Yukawa uses the term “anti-neutrino”.
64. Fermi was already an expert at this type of calculation, having lectured on it at the Symposium for Theoretical Physics of the 1930 Summer Session of the University of Michigan at
Ann Arbor. Rev. Mod. Phys. 4 (1932), 87-132 (i.e. for the electromagnetic field).
65. The reference and a translation of the introduction are given in Appendix 11.
66. See ref. 20, p. 155.
67. S. Tomonaga, H. Yukawa, S. Taketani, Y. Fujimoto, S. Sakata, in The Creation ofScience
and Peace (Iwanami, 1961); translation by R. Yoshida. (Originally published in Kagaku,
April 1961).
68. AHQP. Interview by John A. Wheeler in Kyoto, July, 1962.
69. Now President of the Science Council of Japan and Director Emeritus of the Institute of
Plasma Physics at the University of Nagoya. I am greatly indebted to Prof. Husimi for
discussions in Tokyo in October, 1978.
128
Laurie
M. Brown
70. See ref. 30. Another excellent discussion of the period to about 1930 is Shigeru Nakayama,
Characteristics of Scientific Development in Japan (four lectures given at and published by
The Centre for the Study of Science, Technology and Development, CSIR, New Delhi,
India, 1977).
71. See ref. 41. Sakata adds that at Osaka, anew Imperial University, “bureaucratism was not
too marked”. His remarks apply to both theoretical and experimental research. Another
student of Yukawa, Minoru Kobayasi, agreed with the general thesis but said:
“Kyoto was known as a conservative university, but it was very open to new ideas and
allowed young people to study them. Tamaki [the mentor of Yukawa and Tomonaga
after their graduation] worked on relativity and hydromechanics and showed no interest in quantum theory, but he was generous to young people who worked on quantum theory.”
72. Three months after his arrival, on 6 April 1929, Nishina wrote to Samuel A. Goudsmit, an
old friend from Copenhagen days, whom he visited at Ann Arbor, Michigan, on his way
home. He wrote that because of the 1923 earthquake, Tokyo was unrecognizable to him,
and “At first it was interesting to see Japanese customs, houses and cloths [sic], but now they
do not interest my any more.” Nishina asks the news from Europe, “from which a great
distance isolates me totally.”
73. MasaTakeuchi, “Remembrance of Studies of Mesons in the Cosmic Rays”, Shizen (Nature),
July 1975, pp. 52-59, translated by R. Yoshida.
74. The late Tetu Hirosige in “Social Conditions for Prewar Japanese Research in Nuclear
Physics” (see ref. 30) stresses the support given to nuclear and cosmic ray research by the
Japan Society for the Promotion of Scientific Research (Nihon Gakujutsu Shinkokai),
established in December 1932. In particular their Subcommittee No. 10 (for cosmic rays)
had funds to distribute to university chairs and to Riken which “were extraordinarily large
for those days.” With their support the number of papers related to nuclear physics that
were presented at the Annual Meetings of the Physico-Mathematical Society of Japan grew
from two in 1933 (one by Yukawa and one by Nishina and Tomonaga) to forty-two in 1942,
the latter amounting to 25% of all papers presented at that meeting.
75. The importance of Riken was emphasized in discussions and workshops conducted in Japan
during Sept.-Oct., 1978 and May, 1979 by a group of Japanese and American physicists and
historians, including myself. The former Riken workers participating in these discussions
included: M. Kobayasi, S.Tomonaga, M. Takeuchi, H. Tamaki, C. Ishii, 0. Minakawa. The
former Osaka University members participating included: Y. Tanikawa, M.Taketani, K.
Husimi. Others involved were: Y. Nambu, 2.Maki, S. Hayakaya, R. Kawabe, M.Konuma,
S. Nakamura, T. Takabayashi, Y. Fujimoto, and T. Tsuji. I wish to thank all of these
collaborators and the National Science Foundation, USA, and the Japan Society for the
Promotion of Science for grants supporting this work, and to thank the Research Institute
for Fundamental Physics at Kyoto University and its Director Humitaka Sat0 for extending
warm hospitality to me.
76. This was Hidehiko Tamaki, not Kajuro Tamaki, the Kyoto University professor who died in
1939 and was succeeded by Yukawa.
77. Tomonaga describes his research at Riken, including candid comments, in “Reminiscences
of my research - from old records”, Butsuri (Bull. Jap. Phys. SOC.) 32, vol. 10 (1977),
762-773; unpublished translation by Noriko Eguchi.
Yukawas’s Prediction of the Meson
129
78. This was a smaller private research foundation, begun in 1961 by Seiji Shiomi. See Itakura
and Yagi, “The Japanese Research System”, ref. 30.
79. See ref. 41.
80. For Italian physics see Emilio Segrt, Enrico Fermi, Physicist (U. of Chicago, 1970) and
Gerald Holton, “Fermi’s group and the recapture of Italy’s place in physics,” in The Scien.
tific Irnaginarion: Case Srudies (Cambridge, 1978), pp. 155-198.
81. According to H. A. Bethe and R. F. Bacher, Rev. Mod. Pkys 8 (1936), p. 201, Heisenberg
made this suggestion first in lectures (unpublished) at the Cavendish Laboratory, Cambridge, in 1934. See also W. Heisenberg, Zeeman Verhandelingen (The Hague, 1935),
108-116. Heisenberg thanks Fermi for making the suggestion (by private letter) that the
electron and neutrino may give rise to exchange forces.
82. Ig. Tamm, Nature 133, 981 (1934); D. Iwanenko, ibid., 981. The negative result of Tamm
and Iwanenko did not chill the temptation. At the London Conference, 1934 [Papers and
Discussions, Internationol Conference on Physics, London, I934 (Cambridge, 1935)], Bethe
proposed a modification of Fermi‘s beta decay Hamiltonian, in part to obtain a stronger
Heisenberg exchange force. In 1936, Bethe and Bacher (ref. 81) use a modified Fermi
theory, containing derivatives of the fields (Konopinski-Uhlenbeck form); but they still
obtain binding forces that are too weak. In spite of the gross disagreement, they maintain
that “the general idea of a connection between B-emission and nuclear forces is so attractive
that one would be very reluctant to give it up.” (See also Mukherji, ref. 2, p. 34 for a
discussion of this point). A. Nordsieck [Phys. Rev. 46 (1934), 234-51 calculates the scattering of neutrons by protons, assuming that the force is given by electron-neutrino exchange,
and finds absurdly small cross-sections. Wick tries the same approach, intending to “shed a
bit of light” on the proton’s magnetic moment. [G. C. Wick, Rend. Accademia dei Lincei (6)
21 (1935), 176173.1 Assuming that the proton spends a certain fraction of its time virtually
dissociated into neutron, positron, and antineutrino, it should have the large Bohr magneton, e h / h c (rather than the nuclear magneton) during this time. By modifying Fermi’s
interaction, Wick claims to obtain reasonable values. His motivation is clear: “It would
evidently be notable progress to be able to treat the exchange interaction and the theory ofp
rays from a unified point of view.” In some cases, ideas similar to those of Nordsieck and
Wick were later applied in meson theory, with the meson replacing the electron-neutrino
pair.
83. Unless otherwise indicated, quotations in this section and the following are from ref. 1.
84. The word scalar is used in the three-dimensional sense. Yukawa’s nuclear potential transforms under Lorentz transformations as the fourth component of a four-vector, and not as a
relativisric (i.e., four-dimensional) scalar. The U-quanta (or mesons) have spin zero, but are
not what were later called scalar mesons.
85. More exactly, the said solutions (both the electromagnetic and nuclear ones) are valid e.rcept
in the infinitesimal neighborhood of the origin. The physical interpretation (in either case) is
that there is a point “charge” located at the origin.
86. In modem meson theory the nucleons are described (at least in principle) by the Dirac field,
and the anomalous magnetic moments are considered to be a consequence of the interaction
of the nucleons with the meson field.
87. More precisely, the field must have more than one real component. (Being complex is
equivalent to having two real components.)
9 Centaurus XXV
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Laurie M . Brown
88. Yukawa calls these matrices r,, 7 * , T, (as they are usually designated today). Heisenberg’s
@-valuecorresponds to 73rwhich has the value +1 for neutron, -1 for proton.
89. The spin plays no dynamical role in this, the first of the meson papers. Yukawa says he will
ignore it for the heavy particles. It does enter in symmetry considerations.
90. The interaction energyJ(r) is proportional tog2, and the same sign of the “charge”g (either
positive or negative) must be used both for absorption and emission of the U-field, sinceg is
not associated with either proton or neutron state, but with their product.
91. The estimates are made by comparing certain predictions of the theory with experiment
(e.g., the deuteron binding energy and the n-p scattering cross-section). Yukawa acknowledges assistance from Tomonaga in making these comparisons.
92. See Heisenberg and Pauli, ref. 37; also ref. 61 and the text thereto. The second quantization
of the U-field, which parallels the quantization of the electromagnetic field, leads to
Bose-Einstein statistics for the U-quanta.
93. The connection between force range and the mass of its quanta is taken for granted today,
but it was not obvious before Yukawa’s work. Several years later, G. C. Wick gave an
elementary discussion of this relation, based upon the uncertainty principle: Nature I42
(1938), 994.
94. Some readers may find it puzzling to consider the neutron and proton as a “pair”, since they
appear successively, rather than simultaneously. From the standpoint of quantum field
theory, however, the important point is that a three fold product of field operators appears
in the strong interaction, as it does in the weak. In the strong case, it is neutron-proton-U-quantum; in the weak case, it is electron-antineutrino-U-quantum.
Three-particle
interactions that involve the emission or absorption of a massive boson are generally called
“Yukawa interactions”.
95. In the internal conversion process an excited nucleus gives up its excitation energy to an
atomic electron, the latter being ejected from the atom. A y ray is supposed to carry the
energy and momentum from the nucleus to the atomic electron, but it is not observable. (We
have corrected some obvious misprints in the text quoted from Yukawa).
96. pk and tpk are relativistic field operators of spin * / z neutrino and electron.
97. Yukawa and S. Sakata calculated the spontaneous half-life of the meson after seeing a letter
in Narure, where this consequence of the theory was noted by Bhabha. (This is stated by
Yukawa in the Wheeler interview, ref. 68. The letter in question is probably: H. I. Bhabha,
Nurure 141 (1938). 117-118).
and 471-472; T. H. Johnson, Phys. Rev. 45
98. G. H. Huxley, Nature I34 (1934), 41-19
(1934), 569-585. Jonhnson concluded from his observations that the primary cosmic radiation was “largely and probably exclusively positive”.
99. Tanikawa, ref. 19.
100. See ref. 38 and the text thereto. See ref. 16, pp. 170-172 for another discussion of this
point.
101. See L. M. Brown, ref. 44.
102. P. A. M. Dirac, “The Prediction of Antimatter”, The 1st H. R . Crane Lecture, April 17,
1978 at University of Michigan, Ann Arbor.
103. There is an interesting analogy between the idea that different laws of physics apply at
different space-time scales and the idea that science itself is culture-bound (or put
otherwise, that “all science is ethnoscience”).
Yukawus’s Prediction of the Meson
131
104. Heisenberg, to Pauli, April 5, 1938 (Pauli Letter Collection). Late in life he argued that we
must learn to do without pictures, for “the antinomy of the smallest dimensions is solved in
particle physics in a very subtle manner, of which neither Kant nor the ancient
philosophers could have thought: The word ‘dividing’ loses its meaning.” Werner Heisenberg, “The Nature of elementary particles”, Physics Today March 1976, pp. 32-39.
105. U o n Brillouin , “Individuality of elementary particles - Quantum statistics. Pauli’s principle,” in New Theories in Physics, Conference held in Warsaw, May 30 to June 3, 1938;
(International Institute of Intellectual Co-operation, Paris, 1939), pp. 119-172.
106. Brillouin afterwards remarks parenthetically that Yukawa’s hypothesis was “also arrived at
independently” by E. C. G. Stueckelberg. This is claimed by Stueckelberg, in the second
reference to Yukawa’s work, outside of Japan (ref. 9). After noting the cosmic ray evidence (ref. 10) for a “heavy electron”, the letter says: “The writer wishes to call attention
to an explanation of the nuclear forces, given as early as 1934, by Yukawa, which predicts
particles of this sort. Independently of Yukawa the writer arrived at the same conclu” This may be true, but it is not supported by an examination of Stueckelberg’s
published works that precedes his letter to the Editor of the Physical Review. [These are as
follows: Nuture 137, (1936). 1032; Helv. Phys. Acta. 9, (1936), 389-404;ibid. , 533-554;
C.R. de la SOC.phys. et sc. nut. GenPve 53 (1936), 64. (The last I have not seen.)] On the
basis of the published record, Stueckelberg’s claim seems to be the following: A “unitary
field theory” was proposed (quotations here are from the Nature letter) under the
hypothesis “that positive electron, neutrino, positive proton and neutron are four different
quantum states of one elementary particle.” Also: “Such an assumption would be trivial
unless transitions between the different states occur.” The unitary field is then described by
a 16 component Dirac spinor. Electromagnetic effects can be included “as soon as the
neutrino theory of light can be formulated in a satisfactory way.” The nuclear exchange
force, related to the neutron-proton transition is to be that of Majorana (ref. 53). The only
reference to a new light charged particle appears in the second Hefvetica article, on p. 534:
“Man kann daher die Fermi’s&he Theorie formal analog der Wechselwirkung nvischen
electromagnetischem Feld und Dirac- electron behandeln . .” (my emphasis). The particle
is thus seen as a formul analogue of the photon, allowing the application to the Fermi
rheory of a previously developed form of perturbation theory. Stueckelberg’stheory of the
nuclear force is thus a version of the “Fermi field” theory of nuclear forces. As befits a
“unitary theory”, Stueckelberg has only one coupling constant, that of Fermi, and his
theory lacks the strong coupling constant of Yukawa.
107. Thomas S. Kuhn, The Structure of Scientific Revolutions. 2110ed. (Chicago Univ. Press,
1970).
108. J. L. Heilbron, “Quantum Historiography and the AHQP”, History of Science 7 (1968),
90-111.
109. Shoichi Sakata was the son of Mikita Sakata, who was the secretary of Taro Katsura,
Premier of Japan during the Russo-Japanese War.
110. See ref. 41. Also: W. Heitler and F. Sauter, Nature 132, (1933), 892.
111. H. Yukawa and S. Sakata, “On the Theory of Internal Pair Production”, Proc. Phys. Math. SOC.Japan I7 (1935), 394-407. This was Yukawa’s second and Sakata’s first paper.
Results were compared with an experiment done with a Ru(B+C) source: A. I. Alichanow
and H. S. Kosodaew, Zeit. f. Phys. 90 (1934), 249.
132
Laurie M. Brown
112. H. Yukawa and S. Sakata, “On the Theory of the B-Disintegration and the Allied
Phenomenon”, Proc. Phys. - Math. SOC. of Japan I 7 (1935), 4 6 7 4 6 9 . The K-capture
process was discovered later by Christian M ~ l l e r“On
,
the Capture of Orbital Electrons by
Nuclei”, Phys. Rev. 51 (1937), 84-85. Meller does not refer to Yukawa and Sakata. The
experimental verification of the K-capture process was given by Louis W. Alvarez, Phys.
Rev. 54 (193&), 486.
113 See ref. 41.
114 Sakata, “On Interpretation of the Quantum Mechanics”, in Supp. Prog. Theor. Phys. No.
50 (1971), 171-184. Originally in Japanese in Kugaku 29 (1959), pp. 6 2 6 4 3 1 .
115. Taketani, ref. 30.
116 S. Sakata, “The Background to the Development of Yukawa’s Meson Theory”, Shizen
(Nature), August 1946; reprinted in S. Sakata, Coffected Essays, Vol. I, Physics and
Method (Iwanami Shoten, 1972), pp. 97-107; unpublished translation by R. Kawabe.
117. M. Taketani, “The Meson Theory and the Methodology of Three Stages”, in Hisrory of
Japanese Physics, Vof. I , The Physical Society of Japan Edition (Tokai University Press,
1978), Tetsuo Tsuji, editor; translation by Y. Fujimoto and M. Nagasaki.
118. Sosuke Takauchi, Order und Chaos (Kosakusha, 1974), in Japanese; enlarged and revised
edition in 1979.
119. This is the idea that the cosmic ray meson (muon) is a weakly interacting decay product of
the Yukawa meson (pion). A complete documentation of this idea is lacking, and is being
investigated. Since it is a complex question requiring a full study, I will merely remark here
that it was first proposed in early 1942 by Yasutaka Tanikawa and discussed (in at least
two versions) by him and others at the 41st Meeting of Riken on June 12, 1942. The
history of the two-meson (and two-neutrino) theory is discussed by M. Konuma,
Soryushiron kenkyu (Particle Research) 38 (1968), p. 482.
120. This idea is similar to Heisenberg’s; see ref. 104.
121. See ref. 10 for the first announcements. For background and brief history see, e.g., Satio
Hayakawa, Cosmic Ray Physics (Wiley Interscience, 1969), Chapter I. For additional
material on this section see Mukherji, ref. 2.
122 Ref. 11. None of the first experimental papers mentioned Yukawa (not even the Japanese
one). Yukawa’s note pointed out: “The most important and at the same time inevitable
consequence of the theory was that the field was to be accompanied by new sorts of quanta
obeying Bose statistics and each having the elementary charge +e or -e and the proper
mass m u about 200 times as large as the electron mass.” Although there is no doubt that
most (if not all) theoreticians assumed the muon to be Yukawais meson, this played no role
in its discovery. Thus S. H. Neddermeyer says “the muon, like the positron, was a purely
experimental discovery in the sense that it was made entirely independently of any
theoretical considerations of what particles should or should not exist.” F. F. Deery and S.
H. Neddermeyer, Phys. Rev. 121 (1961), 1803-1814, Note 1.
123 N. Kemmer, “The Impact of Yukawa’s Meson Theory on Workers in Europe - A Reminiscence”, Supp. of the Prog. of Theor, Phys., Commemoration Issue for the 30th Anniversary of rhe Meson Theory by Dr. H . Yukawa, 1965, 602-608. Most of this passage is
quoted also by Mukherji, ref. 2.
124. See ref. 105.